Abstract
We determine the lens spaces that arise by integer Dehn surgery along a knot in the three-sphere. Specifically, if surgery along a knot produces a lens space, then there exists an equivalent surgery along a Berge knot with the same knot Floer homology groups. This leads to sharp information about the genus of such a knot. The arguments rely on tools from Floer homology and lattice theory. They are primarily combinatorial in nature.
-
[baileyrolfsen]
J. Bailey and D. Rolfsen, "An unexpected surgery construction of a lens space," Pacific J. Math., vol. 71, iss. 2, pp. 295-298, 1977.
@article {baileyrolfsen, MRKEY = {0488061},
AUTHOR = {Bailey, James and Rolfsen, Dale},
TITLE = {An unexpected surgery construction of a lens space},
JOURNAL = {Pacific J. Math.},
FJOURNAL = {Pacific Journal of Mathematics},
VOLUME = {71},
YEAR = {1977},
NUMBER = {2},
PAGES = {295--298},
ISSN = {0030-8730},
MRCLASS = {57A10 (55A25)},
MRNUMBER = {0488061},
MRREVIEWER = {Deborah L. Goldsmith},
ZBLNUMBER = {0349.55004},
ZBLNUMBER = {0319.55008},
URL = {http://projecteuclid.org/euclid.pjm/1102811428},
} -
[baker:poincare] K. L. Baker, The Poincaré homology sphere and almost-simple knots in lens spaces, 2011.
@misc{baker:poincare,
author={Baker, Kenneth L.},
TITLE={The {P}oincaré homology sphere and almost-simple knots in lens spaces},
ARXIV={1111.6877},
YEAR={2011},
} -
[baker:comm] K. L. Baker, Private communication, 2011.
@misc{baker:comm,
author={Baker, Kenneth L.},
TITLE={Private communication},
YEAR={2011},
SORTYEAR={2012},
} -
[bgh:lens]
K. L. Baker, E. J. Grigsby, and M. Hedden, "Grid diagrams for lens spaces and combinatorial knot Floer homology," Int. Math. Res. Not., vol. 2008, iss. 10, p. I.
@article {bgh:lens, MRKEY = {2429242},
AUTHOR = {Baker, Kenneth L. and Grigsby, J. Elisenda and Hedden, Matthew},
TITLE = {Grid diagrams for lens spaces and combinatorial knot {F}loer homology},
JOURNAL = {Int. Math. Res. Not.},
FJOURNAL = {International Mathematics Research Notices. IMRN},
SORTYEAR = {2008},
NUMBER = {10},
PAGES = {Art. ID rnm024, 39},
ISSN = {1073-7928},
MRCLASS = {57M27 (57R58)},
MRNUMBER = {2429242},
MRREVIEWER = {Sabin Cautis},
DOI = {10.1093/imrn/rnn024},
VOLUME = {2008},
ZBLNUMBER = {1168.57009},
} -
[berge:solidtorus]
J. Berge, "The knots in $D^2\times S^1$ which have nontrivial Dehn surgeries that yield $D^2\times S^1$," Topology Appl., vol. 38, iss. 1, pp. 1-19, 1991.
@article {berge:solidtorus, MRKEY = {1093862},
AUTHOR = {Berge, John},
TITLE = {The knots in {$D\sp 2\times S\sp 1$} which have nontrivial {D}ehn surgeries that yield {$D\sp 2\times S\sp 1$}},
JOURNAL = {Topology Appl.},
FJOURNAL = {Topology and its Applications},
VOLUME = {38},
YEAR = {1991},
NUMBER = {1},
PAGES = {1--19},
ISSN = {0166-8641},
CODEN = {TIAPD9},
MRCLASS = {57M25 (57N10)},
MRNUMBER = {1093862},
MRREVIEWER = {Chichen M. Tsau},
DOI = {10.1016/0166-8641(91)90037-M},
ZBLNUMBER = {0725.57001},
} -
[berge:ppknots] J. Berge, The simple closed curves in genus two Heegaard surfaces of $S^3$ which are double-primitives, 2010.
@misc{berge:ppknots,
author = {Berge, John},
TITLE = {The simple closed curves in genus two {H}eegaard surfaces of {$S^3$} which are double-primitives},
NOTE={unpublished manuscript},
SORTYEAR={2020},
YEAR={2010},
} -
[berge:lens] J. Berge, Some knots with surgeries yielding lens spaces, c. 1990.
@misc{berge:lens,
author={Berge, John},
TITLE = {Some knots with surgeries yielding lens spaces},
NOTE={unpublished manuscript},
YEAR={c.~1990},
SORTYEAR={2018},
} -
[brown:changemaker]
J. L. Brown Jr., "Note on complete sequences of integers," Amer. Math. Monthly, vol. 68, pp. 557-560, 1961.
@article {brown:changemaker, MRKEY = {0130207},
AUTHOR = {Brown, Jr., J. L.},
TITLE = {Note on complete sequences of integers},
JOURNAL = {Amer. Math. Monthly},
FJOURNAL = {The American Mathematical Monthly},
VOLUME = {68},
YEAR = {1961},
PAGES = {557--560},
ISSN = {0002-9890},
MRCLASS = {10.60},
MRNUMBER = {0130207},
MRREVIEWER = {L. Mirsky},
ZBLNUMBER = {0115.04305},
DOI = {10.2307/2311150},
} -
[cg:cobordism] A. J. Casson and . C. Gordon, "Cobordism of classical knots," in À la recherche de la Topologie Perdue, Boston, MA: Birkhäuser, 1986, vol. 62, pp. 181-199.
@incollection {cg:cobordism, MRKEY = {0900252},
AUTHOR = {Casson, A. J. and Gordon, C. {\relax{McA}}},
TITLE = {Cobordism of classical knots},
BOOKTITLE = {À la recherche de la Topologie Perdue},
SERIES = {Progr. Math.},
VOLUME = {62},
PAGES = {181--199},
PUBLISHER = {Birkhäuser},
ADDRESS = {Boston, MA},
YEAR = {1986},
MRCLASS = {57R90 (57M25)},
MRNUMBER = {0900252},
ZBLNUMBER = {0597.57001},
} -
[cgls:cyclic]
M. Culler, . C. Gordon, J. Luecke, and P. B. Shalen, "Dehn surgery on knots," Ann. of Math., vol. 125, iss. 2, pp. 237-300, 1987.
@article {cgls:cyclic, MRKEY = {0881270},
AUTHOR = {Culler, Marc and Gordon, C. {\relax{McA}} and Luecke, J. and Shalen, Peter B.},
TITLE = {Dehn surgery on knots},
JOURNAL = {Ann. of Math.},
FJOURNAL = {Annals of Mathematics. Second Series},
VOLUME = {125},
YEAR = {1987},
NUMBER = {2},
PAGES = {237--300},
ISSN = {0003-486X},
CODEN = {ANMAAH},
MRCLASS = {57N12 (57M25 57M40)},
MRNUMBER = {0881270},
MRREVIEWER = {John Hempel},
DOI = {10.2307/1971311},
ZBLNUMBER = {0633.57006},
} -
[donald-owens:chislice] A. Donald and B. Owens, Concordance groups of links, 2012.
@misc{donald-owens:chislice,
author={Donald, A. and Owens, B.},
TITLE = {Concordance groups of links},
ARXIV={1203.3238},
YEAR={2012},
} -
[d:thma]
S. K. Donaldson, "The orientation of Yang-Mills moduli spaces and $4$-manifold topology," J. Differential Geom., vol. 26, iss. 3, pp. 397-428, 1987.
@article {d:thma, MRKEY = {0910015},
AUTHOR = {Donaldson, S. K.},
TITLE = {The orientation of {Y}ang-{M}ills moduli spaces and {$4$}-manifold topology},
JOURNAL = {J. Differential Geom.},
FJOURNAL = {Journal of Differential Geometry},
VOLUME = {26},
YEAR = {1987},
NUMBER = {3},
PAGES = {397--428},
ISSN = {0022-040X},
CODEN = {JDGEAS},
MRCLASS = {57R19 (32C10 32G13 57N13 57R55 58E15)},
MRNUMBER = {0910015},
MRREVIEWER = {Nicholas Buchdahl},
URL = {http://projecteuclid.org/euclid.jdg/1214441485},
ZBLNUMBER = {0683.57005},
} -
[elkies] N. D. Elkies, "A characterization of the ${\bf Z}^n$ lattice," Math. Res. Lett., vol. 2, iss. 3, pp. 321-326, 1995.
@article {elkies, MRKEY = {1338791},
AUTHOR = {Elkies, Noam D.},
TITLE = {A characterization of the {${\bf Z}\sp n$} lattice},
JOURNAL = {Math. Res. Lett.},
FJOURNAL = {Mathematical Research Letters},
VOLUME = {2},
YEAR = {1995},
NUMBER = {3},
PAGES = {321--326},
ISSN = {1073-2780},
MRCLASS = {11H06 (57R55)},
MRNUMBER = {1338791},
MRREVIEWER = {Andrew Granville},
ZBLNUMBER = {0855.11032},
} -
[fs:comm] R. Fintushel and R. J. Stern, Private communication, 2012.
@misc{fs:comm,
author={Fintushel, Ronald and Stern, Ronald J.},
TITLE={private communication},
YEAR={2012},
} -
[fs:lenssurgery]
R. Fintushel and R. J. Stern, "Constructing lens spaces by surgery on knots," Math. Z., vol. 175, iss. 1, pp. 33-51, 1980.
@article {fs:lenssurgery, MRKEY = {0595630},
AUTHOR = {Fintushel, Ronald and Stern, Ronald J.},
TITLE = {Constructing lens spaces by surgery on knots},
JOURNAL = {Math. Z.},
FJOURNAL = {Mathematische Zeitschrift},
VOLUME = {175},
YEAR = {1980},
NUMBER = {1},
PAGES = {33--51},
ISSN = {0025-5874},
CODEN = {MAZEAX},
MRCLASS = {57N10 (57M25)},
MRNUMBER = {0595630},
MRREVIEWER = {W. D. Neumann},
DOI = {10.1007/BF01161380},
ZBLNUMBER = {0425.57001},
} -
[fs:sigma237]
R. Fintushel and R. J. Stern, "A $\mu$-invariant one homology $3$-sphere that bounds an orientable rational ball," in Four-Manifold Theory, Providence, RI: Amer. Math. Soc., 1984, vol. 35, pp. 265-268.
@incollection {fs:sigma237, MRKEY = {0780582},
AUTHOR = {Fintushel, Ronald and Stern, Ronald J.},
TITLE = {A {$\mu$}-invariant one homology {$3$}-sphere that bounds an orientable rational ball},
BOOKTITLE = {Four-Manifold Theory},
VENUE={{D}urham, {N}.{H}., 1982},
SERIES = {Contemp. Math.},
VOLUME = {35},
PAGES = {265--268},
PUBLISHER = {Amer. Math. Soc.},
ADDRESS = {Providence, RI},
YEAR = {1984},
MRCLASS = {57N13 (57R65)},
MRNUMBER = {0780582},
MRREVIEWER = {Shmuel Weinberger},
DOI = {10.1090/conm/035/780582},
ZBLNUMBER = {0566.57006},
} -
[froyshov:poincare] K. A. Frøyshov, "The Seiberg-Witten equations and four-manifolds with boundary," Math. Res. Lett., vol. 3, iss. 3, pp. 373-390, 1996.
@article {froyshov:poincare, MRKEY = {1397685},
AUTHOR = {Frøyshov, Kim A.},
TITLE = {The {S}eiberg-{W}itten equations and four-manifolds with boundary},
JOURNAL = {Math. Res. Lett.},
FJOURNAL = {Mathematical Research Letters},
VOLUME = {3},
YEAR = {1996},
NUMBER = {3},
PAGES = {373--390},
ISSN = {1073-2780},
MRCLASS = {57R57 (57N13 57R15)},
MRNUMBER = {1397685},
MRREVIEWER = {Weimin Chen},
ZBLNUMBER = {0872.57024},
} -
[gabai:solidtorus]
D. Gabai, "Surgery on knots in solid tori," Topology, vol. 28, iss. 1, pp. 1-6, 1989.
@article {gabai:solidtorus, MRKEY = {0991095},
AUTHOR = {Gabai, David},
TITLE = {Surgery on knots in solid tori},
JOURNAL = {Topology},
FJOURNAL = {Topology. An International Journal of Mathematics},
VOLUME = {28},
YEAR = {1989},
NUMBER = {1},
PAGES = {1--6},
ISSN = {0040-9383},
CODEN = {TPLGAF},
MRCLASS = {57M25 (57R30)},
MRNUMBER = {0991095},
MRREVIEWER = {Cameron McA. Gordon},
DOI = {10.1016/0040-9383(89)90028-1},
ZBLNUMBER = {0678.57004},
} -
[gerstein]
L. J. Gerstein, "Nearly unimodular quadratic forms," Ann. of Math., vol. 142, iss. 3, pp. 597-610, 1995.
@article {gerstein, MRKEY = {1356782},
AUTHOR = {Gerstein, Larry J.},
TITLE = {Nearly unimodular quadratic forms},
JOURNAL = {Ann. of Math.},
FJOURNAL = {Annals of Mathematics. Second Series},
VOLUME = {142},
YEAR = {1995},
NUMBER = {3},
PAGES = {597--610},
ISSN = {0003-486X},
CODEN = {ANMAAH},
MRCLASS = {11E12 (11H55)},
MRNUMBER = {1356782},
MRREVIEWER = {Rudolf Scharlau},
DOI = {10.2307/2118555},
ZBLNUMBER = {0842.11012},
} -
[ghiggini]
P. Ghiggini, "Knot Floer homology detects genus-one fibred knots," Amer. J. Math., vol. 130, iss. 5, pp. 1151-1169, 2008.
@article {ghiggini, MRKEY = {2450204},
AUTHOR = {Ghiggini, Paolo},
TITLE = {Knot {F}loer homology detects genus-one fibred knots},
JOURNAL = {Amer. J. Math.},
FJOURNAL = {American Journal of Mathematics},
VOLUME = {130},
YEAR = {2008},
NUMBER = {5},
PAGES = {1151--1169},
ISSN = {0002-9327},
CODEN = {AJMAAN},
MRCLASS = {57M25 (57R58)},
MRNUMBER = {2450204},
DOI = {10.1353/ajm.0.0016},
ZBLNUMBER = {1149.57019},
} -
[gt:lenssurgery]
H. Goda and M. Teragaito, "Dehn surgeries on knots which yield lens spaces and genera of knots," Math. Proc. Cambridge Philos. Soc., vol. 129, iss. 3, pp. 501-515, 2000.
@article {gt:lenssurgery, MRKEY = {1780501},
AUTHOR = {Goda, Hiroshi and Teragaito, Masakazu},
TITLE = {Dehn surgeries on knots which yield lens spaces and genera of knots},
JOURNAL = {Math. Proc. Cambridge Philos. Soc.},
FJOURNAL = {Mathematical Proceedings of the Cambridge Philosophical Society},
VOLUME = {129},
YEAR = {2000},
NUMBER = {3},
PAGES = {501--515},
ISSN = {0305-0041},
CODEN = {MPCPCO},
MRCLASS = {57M25 (57N10)},
MRNUMBER = {1780501},
MRREVIEWER = {Daniel Matignon},
DOI = {10.1017/S0305004100004692},
ZBLNUMBER = {1029.57005},
} -
[greene:3braids] J. Greene, On closed 3-braids with unknotting number one, 2009.
@misc{greene:3braids,
author = {Greene, Joshua},
TITLE={On closed 3-braids with unknotting number one},
ARXIV={0902.1573},
YEAR={2009},
} -
[greene:cabling] J. Greene, L-space surgeries, genus bounds, and the cabling conjecture, 2010.
@misc{greene:cabling,
author={Greene, Joshua},
TITLE={L-space surgeries, genus bounds, and the cabling conjecture},
ARXIV={1009.1130},
YEAR={2010},
} -
[greene:mutation] J. Greene, Lattices, graphs, and Conway mutation, 2011.
@misc{greene:mutation,
author={Greene, Joshua},
TITLE={Lattices, graphs, and {C}onway mutation},
ARXIV={1103.0487},
YEAR={2011},
} -
[gj:slicepretzels]
J. Greene and S. Jabuka, "The slice-ribbon conjecture for 3-stranded pretzel knots," Amer. J. Math., vol. 133, iss. 3, pp. 555-580, 2011.
@article {gj:slicepretzels, MRKEY = {2808326},
AUTHOR = {Greene, Joshua and Jabuka, Stanislav},
TITLE = {The slice-ribbon conjecture for 3-stranded pretzel knots},
JOURNAL = {Amer. J. Math.},
FJOURNAL = {American Journal of Mathematics},
VOLUME = {133},
YEAR = {2011},
NUMBER = {3},
PAGES = {555--580},
ISSN = {0002-9327},
CODEN = {AJMAAN},
MRCLASS = {57M25 (57N70)},
MRNUMBER = {2808326},
MRREVIEWER = {Charles Livingston},
DOI = {10.1353/ajm.2011.0022},
ZBLNUMBER = {1225.57006},
} -
[hedden:berge]
M. Hedden, "On Floer homology and the Berge conjecture on knots admitting lens space surgeries," Trans. Amer. Math. Soc., vol. 363, iss. 2, pp. 949-968, 2011.
@article {hedden:berge, MRKEY = {2728591},
AUTHOR = {Hedden, Matthew},
TITLE = {On {F}loer homology and the {B}erge conjecture on knots admitting lens space surgeries},
JOURNAL = {Trans. Amer. Math. Soc.},
FJOURNAL = {Transactions of the American Mathematical Society},
VOLUME = {363},
YEAR = {2011},
NUMBER = {2},
PAGES = {949--968},
ISSN = {0002-9947},
CODEN = {TAMTAM},
MRCLASS = {57M25 (57M27 57R58)},
MRNUMBER = {2728591},
MRREVIEWER = {Adam M. Lowrance},
DOI = {10.1090/S0002-9947-2010-05117-7},
ZBLNUMBER = {1229.57006},
} -
[kervairemilnor] M. A. Kervaire and J. W. Milnor, "On $2$-spheres in $4$-manifolds," Proc. Nat. Acad. Sci. U.S.A., vol. 47, pp. 1651-1657, 1961.
@article {kervairemilnor, MRKEY = {0133134},
AUTHOR = {Kervaire, Michel A. and Milnor, John W.},
TITLE = {On {$2$}-spheres in {$4$}-manifolds},
JOURNAL = {Proc. Nat. Acad. Sci. U.S.A.},
FJOURNAL = {Proceedings of the National Academy of Sciences of the United States of America},
VOLUME = {47},
YEAR = {1961},
PAGES = {1651--1657},
ISSN = {0027-8424},
MRCLASS = {57.20},
MRNUMBER = {0133134},
MRREVIEWER = {A. Haefliger},
ZBLNUMBER = {0107.40303},
} -
@misc{kirby:problems, MRKEY = {1470751},
AUTHOR={Rob Kirby},
TITLE = {Problems in low-dimensional topology},
URL={math.berkeley.edu/~kirby/problems.ps.gz},
YEAR={2010},
} -
[kmos]
P. Kronheimer, T. Mrowka, P. Ozsváth, and Z. Szabó, "Monopoles and lens space surgeries," Ann. of Math., vol. 165, iss. 2, pp. 457-546, 2007.
@article {kmos, MRKEY = {2299739},
AUTHOR = {Kronheimer, P. and Mrowka, T. and Ozsv{á}th, P. and Szab{ó},
Z.},
TITLE = {Monopoles and lens space surgeries},
JOURNAL = {Ann. of Math.},
FJOURNAL = {Annals of Mathematics. Second Series},
VOLUME = {165},
YEAR = {2007},
NUMBER = {2},
PAGES = {457--546},
ISSN = {0003-486X},
CODEN = {ANMAAH},
MRCLASS = {57R58 (57M27 57R57)},
MRNUMBER = {2299739},
MRREVIEWER = {Vicente Mu{ñ}oz},
DOI = {10.4007/annals.2007.165.457},
ZBLNUMBER = {1204.57038},
} -
[ana:thesis]
A. G. Lecuona, "On the slice-ribbon conjecture for Montesinos knots," Trans. Amer. Math. Soc., vol. 364, iss. 1, pp. 233-285, 2012.
@article {ana:thesis, MRKEY = {2833583},
AUTHOR = {Lecuona, Ana G.},
TITLE = {On the slice-ribbon conjecture for {M}ontesinos knots},
JOURNAL = {Trans. Amer. Math. Soc.},
FJOURNAL = {Transactions of the American Mathematical Society},
VOLUME = {364},
YEAR = {2012},
NUMBER = {1},
PAGES = {233--285},
ISSN = {0002-9947},
CODEN = {TAMTAM},
MRCLASS = {57M25 (57N70)},
MRNUMBER = {2833583},
MRREVIEWER = {Nikolai N. Saveliev},
DOI = {10.1090/S0002-9947-2011-05385-7},
ZBLNUMBER = {1244.57017},
} -
[lisca:lens1]
P. Lisca, "Lens spaces, rational balls and the ribbon conjecture," Geom. Topol., vol. 11, pp. 429-472, 2007.
@article {lisca:lens1, MRKEY = {2302495},
AUTHOR = {Lisca, Paolo},
TITLE = {Lens spaces, rational balls and the ribbon conjecture},
JOURNAL = {Geom. Topol.},
FJOURNAL = {Geometry \& Topology},
VOLUME = {11},
YEAR = {2007},
PAGES = {429--472},
ISSN = {1465-3060},
MRCLASS = {57M25 (57M12)},
MRNUMBER = {2302495},
MRREVIEWER = {Darren D. Long},
DOI = {10.2140/gt.2007.11.429},
ZBLNUMBER = {1185.57006},
} -
[lisca:lens2]
P. Lisca, "Sums of lens spaces bounding rational balls," Algebr. Geom. Topol., vol. 7, pp. 2141-2164, 2007.
@article {lisca:lens2, MRKEY = {2366190},
AUTHOR = {Lisca, Paolo},
TITLE = {Sums of lens spaces bounding rational balls},
JOURNAL = {Algebr. Geom. Topol.},
FJOURNAL = {Algebraic \& Geometric Topology},
VOLUME = {7},
YEAR = {2007},
PAGES = {2141--2164},
ISSN = {1472-2747},
MRCLASS = {57M25 (57M12 57N10)},
MRNUMBER = {2366190},
MRREVIEWER = {Dave Auckly},
DOI = {10.2140/agt.2007.7.2141},
ZBLNUMBER = {1185.57015},
} -
[ms:ellipsoids]
D. McDuff and F. Schlenk, "The embedding capacity of 4-dimensional symplectic ellipsoids," Ann. of Math., vol. 175, iss. 3, pp. 1191-1282, 2012.
@article {ms:ellipsoids, MRKEY = {2912705},
AUTHOR = {McDuff, Dusa and Schlenk, Felix},
TITLE = {The embedding capacity of 4-dimensional symplectic ellipsoids},
JOURNAL = {Ann. of Math.},
FJOURNAL = {Annals of Mathematics. Second Series},
VOLUME = {175},
YEAR = {2012},
NUMBER = {3},
PAGES = {1191--1282},
ISSN = {0003-486X},
CODEN = {ANMAAH},
MRCLASS = {53Dxx},
MRNUMBER = {2912705},
DOI = {10.4007/annals.2012.175.3.5},
ZBLNUMBER = {06051270},
} -
[milnor+husemoller] J. Milnor and D. Husemoller, Symmetric Bilinear Forms, New York: Springer-Verlag, 1973, vol. 73.
@book {milnor+husemoller, MRKEY = {0506372},
AUTHOR = {Milnor, John and Husemoller, Dale},
TITLE = {Symmetric Bilinear Forms},
NOTE = {Ergeb. Math. Grenzgeb.},
VOLUME={73},
PUBLISHER = {Springer-Verlag},
ADDRESS = {New York},
YEAR = {1973},
PAGES = {viii+147},
MRCLASS = {15A63 (10C05 57D65)},
MRNUMBER = {0506372},
MRREVIEWER = {Louis H. Kauffman},
ZBLNUMBER = {0292.10016},
} -
[moser:torus]
L. Moser, "Elementary surgery along a torus knot," Pacific J. Math., vol. 38, pp. 737-745, 1971.
@article {moser:torus, MRKEY = {0383406},
AUTHOR = {Moser, Louise},
TITLE = {Elementary surgery along a torus knot},
JOURNAL = {Pacific J. Math.},
FJOURNAL = {Pacific Journal of Mathematics},
VOLUME = {38},
YEAR = {1971},
PAGES = {737--745},
ISSN = {0030-8730},
MRCLASS = {55F55 (57C45)},
MRNUMBER = {0383406},
MRREVIEWER = {Wilbur Whitten},
ZBLNUMBER = {0202.54701},
URL = {http://projecteuclid.org/euclid.pjm/1102969920},
} -
[ni:fibered]
Y. Ni, "Knot Floer homology detects fibred knots," Invent. Math., vol. 170, iss. 3, pp. 577-608, 2007.
@article {ni:fibered, MRKEY = {2357503},
AUTHOR = {Ni, Yi},
TITLE = {Knot {F}loer homology detects fibred knots},
JOURNAL = {Invent. Math.},
FJOURNAL = {Inventiones Mathematicae},
VOLUME = {170},
YEAR = {2007},
NUMBER = {3},
PAGES = {577--608},
ISSN = {0020-9910},
CODEN = {INVMBH},
MRCLASS = {57R58 (57M27 57R30)},
MRNUMBER = {2357503},
MRREVIEWER = {Stanislav Jabuka},
DOI = {10.1007/s00222-007-0075-9},
ZBLNUMBER = {1138.57031},
} -
[ni:erratum]
Y. Ni, "Erratum: Knot Floer homology detects fibred knots," Invent. Math., vol. 177, iss. 1, pp. 235-238, 2009.
@article {ni:erratum, MRKEY = {2507641},
AUTHOR = {Ni, Yi},
TITLE = {Erratum: {K}not {F}loer homology detects fibred knots},
JOURNAL = {Invent. Math.},
FJOURNAL = {Inventiones Mathematicae},
VOLUME = {177},
YEAR = {2009},
NUMBER = {1},
PAGES = {235--238},
ISSN = {0020-9910},
CODEN = {INVMBH},
MRCLASS = {57R58 (57M27 57R30)},
MRNUMBER = {2507641},
DOI = {10.1007/s00222-009-0174-x},
ZBLNUMBER = {1162.57300},
} -
[os:absgr]
P. Ozsváth and Z. Szabó, "Absolutely graded Floer homologies and intersection forms for four-manifolds with boundary," Adv. Math., vol. 173, iss. 2, pp. 179-261, 2003.
@article {os:absgr, MRKEY = {1957829},
AUTHOR = {Ozsv{á}th, Peter and Szab{ó},
Zolt{á}n},
TITLE = {Absolutely graded {F}loer homologies and intersection forms for four-manifolds with boundary},
JOURNAL = {Adv. Math.},
FJOURNAL = {Advances in Mathematics},
VOLUME = {173},
YEAR = {2003},
NUMBER = {2},
PAGES = {179--261},
ISSN = {0001-8708},
CODEN = {ADMTA4},
MRCLASS = {57R58 (57M27)},
MRNUMBER = {1957829},
MRREVIEWER = {Jacob Andrew Rasmussen},
DOI = {10.1016/S0001-8708(02)00030-0},
ZBLNUMBER = {1025.57016},
} -
[os:lens]
P. Ozsváth and Z. Szabó, "On knot Floer homology and lens space surgeries," Topology, vol. 44, iss. 6, pp. 1281-1300, 2005.
@article {os:lens, MRKEY = {2168576},
AUTHOR = {Ozsv{á}th, Peter and Szab{ó},
Zolt{á}n},
TITLE = {On knot {F}loer homology and lens space surgeries},
JOURNAL = {Topology},
FJOURNAL = {Topology. An International Journal of Mathematics},
VOLUME = {44},
YEAR = {2005},
NUMBER = {6},
PAGES = {1281--1300},
ISSN = {0040-9383},
CODEN = {TPLGAF},
MRCLASS = {57R58 (57M27 57R65)},
MRNUMBER = {2168576},
MRREVIEWER = {Thomas E. Mark},
DOI = {10.1016/j.top.2005.05.001},
ZBLNUMBER = {1077.57012},
} -
[r:Lspace] J. Rasmussen, Lens space surgeries and L-space homology spheres, 2007.
@misc{r:Lspace,
author={Rasmussen, J.},
TITLE={Lens space surgeries and {L}-space homology spheres},
ARXIV={0710.2531},
YEAR={2007},
} -
[sr:thesis] S. Rasmussen, A number theoretic result for Berge’s conjecture, 2009.
@misc{sr:thesis,
author={Rasmussen, S.},
TITLE={A number theoretic result for {B}erge's conjecture},
YEAR={2009},
NOTE={Ph.D. thesis, Harvard University},
} -
[riemenschneider] O. Riemenschneider, "Deformationen von Quotientensingularitäten (nach zyklischen Gruppen)," Math. Ann., vol. 209, pp. 211-248, 1974.
@article {riemenschneider, MRKEY = {0367276},
AUTHOR = {Riemenschneider, Oswald},
TITLE = {Deformationen von {Q}uotientensingularitäten (nach zyklischen {G}ruppen)},
JOURNAL = {Math. Ann.},
FJOURNAL = {Mathematische Annalen},
VOLUME = {209},
YEAR = {1974},
PAGES = {211--248},
ISSN = {0025-5831},
MRCLASS = {32C40 (14D15)},
MRNUMBER = {0367276},
MRREVIEWER = {H. B. Laufer},
ZBLNUMBER = {0275.32010},
} -
[saito:lens]
T. Saito, "A note on lens space surgeries: orders of fundamental groups versus Seifert genera," J. Knot Theory Ramifications, vol. 20, iss. 4, pp. 617-624, 2011.
@article {saito:lens, MRKEY = {2796231},
AUTHOR = {Saito, Toshio},
TITLE = {A note on lens space surgeries: orders of fundamental groups versus {S}eifert genera},
JOURNAL = {J. Knot Theory Ramifications},
FJOURNAL = {Journal of Knot Theory and its Ramifications},
VOLUME = {20},
YEAR = {2011},
NUMBER = {4},
PAGES = {617--624},
ISSN = {0218-2165},
MRCLASS = {57M25 (57N10)},
MRNUMBER = {2796231},
DOI = {10.1142/S021821651100939X},
ZBLNUMBER = {1222.57005},
} -
[tange:poincare]
M. Tange, "Lens spaces given from L-space homology 3-spheres," Experiment. Math., vol. 18, iss. 3, pp. 285-301, 2009.
@article {tange:poincare, MRKEY = {2555699},
AUTHOR = {Tange, Motoo},
TITLE = {Lens spaces given from {L}-space homology 3-spheres},
JOURNAL = {Experiment. Math.},
FJOURNAL = {Experimental Mathematics},
VOLUME = {18},
YEAR = {2009},
NUMBER = {3},
PAGES = {285--301},
ISSN = {1058-6458},
MRCLASS = {57M27 (57M25 57R58)},
MRNUMBER = {2555699},
URL = {http://projecteuclid.org/euclid.em/1259158466},
ZBLNUMBER = {1187.57011},
} -
[tange:realization] M. Tange, A complete list of lens spaces constructed by Dehn surgery I, 2010.
@misc{tange:realization,
author = {Tange, Motoo},
TITLE = {A complete list of lens spaces constructed by {D}ehn surgery {I}},
YEAR={2010},
ARXIV={1005.3512},
} -
[tange:comm] M. Tange, Private communication, 2011.
@misc{tange:comm,
author = {Tange, Motoo},
TITLE = {private communication},
YEAR={2011},
} -
[mathematica] S. Wolfram, The Mathematica$^\circledR$ Book, Fourth ed., Wolfram Media, Champaign, IL, 1999.
@book {mathematica, MRKEY = {1721106},
AUTHOR = {Wolfram, Stephen},
TITLE = {The {M}athematica{$^\circledR$} Book},
EDITION = {Fourth},
PUBLISHER = {Wolfram Media, Champaign, IL},
YEAR = {1999},
PAGES = {xxvi+1470},
ISBN = {1-57955-004-5; 0-521-64314-7},
MRCLASS = {68-00 (65-00 68W30)},
MRNUMBER = {1721106},
ZBLNUMBER = {0924.65002},
}