Abstract
In this paper, we give an algorithm to compute the hat version of Heegaard Floer homology of a closed oriented three-manifold. This method also allows us to compute the filtration coming from a null-homologous link in a three-manifold.
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[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},
} -
[Juhasz]
A. Juhász, "Floer homology and surface decompositions," Geom. Topol., vol. 12, iss. 1, pp. 299-350, 2008.
@article {Juhasz, MRKEY = {2390347},
AUTHOR = {Juh{á}sz, Andr{á}s},
TITLE = {Floer homology and surface decompositions},
JOURNAL = {Geom. Topol.},
FJOURNAL = {Geometry \& Topology},
VOLUME = {12},
YEAR = {2008},
NUMBER = {1},
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MRCLASS = {57M27 (57R58)},
MRNUMBER = {2009a:57021},
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DOI = {10.2140/gt.2008.12.299},
ZBLNUMBER = {05256859},
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[Lipshitz]
R. Lipshitz, "A cylindrical reformulation of Heegaard Floer homology," Geom. Topol., vol. 10, pp. 955-1097, 2006.
@article {Lipshitz, MRKEY = {2240908},
AUTHOR = {Lipshitz, Robert},
TITLE = {A cylindrical reformulation of {H}eegaard {F}loer homology},
JOURNAL = {Geom. Topol.},
FJOURNAL = {Geometry and Topology},
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ISSN = {1465-3060},
MRCLASS = {57R58 (57M27)},
MRNUMBER = {2007h:57040},
MRREVIEWER = {Stanislav Jabuka},
DOI = {10.2140/gt.2006.10.955},
ZBLNUMBER = {1130.57035},
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[LipManWang]
R. Lipshitz, C. Manolescu, and J. Wang, "Combinatorial cobordism maps in hat Heegaard Floer theory," Duke Math. J., vol. 145, iss. 2, pp. 207-247, 2008.
@article {LipManWang, MRKEY = {2449946},
AUTHOR = {Lipshitz, Robert and Manolescu, Ciprian and Wang, Jiajun},
TITLE = {Combinatorial cobordism maps in hat {H}eegaard {F}loer theory},
JOURNAL = {Duke Math. J.},
FJOURNAL = {Duke Mathematical Journal},
VOLUME = {145},
YEAR = {2008},
NUMBER = {2},
PAGES = {207--247},
ISSN = {0012-7094},
CODEN = {DUMJAO},
MRCLASS = {57R58 (57R56)},
MRNUMBER = {2009f:57050},
MRREVIEWER = {Burak Ozbagci},
DOI = {10.1215/00127094-2008-050},
ZBLNUMBER = {1153.57027},
} -
[ManOzsSar] C. Manolescu, P. S. Ozsváth, and S. Sarkar, "A combinatorial description of knot Floer homology," Ann. of Math., vol. 169, pp. 633-660, 2009.
@article{ManOzsSar,
author={Manolescu, C. and Ozsváth, P. S. and Sarkar, S.},
TITLE={A combinatorial description of knot Floer homology},
JOURNAL={Ann. of Math.},
VOLUME={169},
YEAR={2009},
PAGES={633--660},
MRNUMBER={2009k:57047},
ZBLNUMBER={pre05578753},
} -
[NiFibred]
Y. Ni, "Knot Floer homology detects fibred knots," Invent. Math., vol. 170, iss. 3, pp. 577-608, 2007.
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AUTHOR = {Ni, Yi},
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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 = {2008j:57053},
MRREVIEWER = {Stanislav Jabuka},
DOI = {10.1007/s00222-007-0075-9},
ZBLNUMBER = {1138.57031},
} -
[N522] Y. Ni, Link Floer homology detects the Thurston norm, 2006.
@misc{N522,
author={Ni, Yi},
TITLE={Link Floer homology detects the Thurston norm},
ARXIV = {math.GT/0604360},
YEAR={2006},
} -
[OSzClosed3M]
P. Ozsváth and Z. Szabó, "Holomorphic disks and topological invariants for closed three-manifolds," Ann. of Math., vol. 159, iss. 3, pp. 1027-1158, 2004.
@article {OSzClosed3M, MRKEY = {2113019},
AUTHOR = {Ozsv{á}th, Peter and Szab{ó},
Zolt{á}n},
TITLE = {Holomorphic disks and topological invariants for closed three-manifolds},
JOURNAL = {Ann. of Math.},
FJOURNAL = {Annals of Mathematics. Second Series},
VOLUME = {159},
YEAR = {2004},
NUMBER = {3},
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ISSN = {0003-486X},
CODEN = {ANMAAH},
MRCLASS = {57M27 (32Q65 57R58)},
MRNUMBER = {2006b:57016},
MRREVIEWER = {Thomas E. Mark},
DOI = {10.4007/annals.2004.159.1027},
ZBLNUMBER = {1073.57009},
} -
[OSzClosed3MApp]
P. Ozsváth and Z. Szabó, "Holomorphic disks and three-manifold invariants: properties and applications," Ann. of Math., vol. 159, iss. 3, pp. 1159-1245, 2004.
@article {OSzClosed3MApp, MRKEY = {2113020},
AUTHOR = {Ozsv{á}th, Peter and Szab{ó},
Zolt{á}n},
TITLE = {Holomorphic disks and three-manifold invariants: properties and applications},
JOURNAL = {Ann. of Math.},
FJOURNAL = {Annals of Mathematics. Second Series},
VOLUME = {159},
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NUMBER = {3},
PAGES = {1159--1245},
ISSN = {0003-486X},
CODEN = {ANMAAH},
MRCLASS = {57M27 (32Q65 57R58)},
MRNUMBER = {2006b:57017},
MRREVIEWER = {Thomas E. Mark},
DOI = {10.4007/annals.2004.159.1159},
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} -
[OSzAbsoluteGrade]
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.
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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},
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NUMBER = {2},
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MRNUMBER = {2003m:57066},
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DOI = {10.1016/S0001-8708(02)00030-0},
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} -
[OSzSmooth4M]
P. Ozsváth and Z. Szabó, "Holomorphic triangles and invariants for smooth four-manifolds," Adv. Math., vol. 202, iss. 2, pp. 326-400, 2006.
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AUTHOR = {Ozsv{á}th, Peter and Szab{ó},
Zolt{á}n},
TITLE = {Holomorphic triangles and invariants for smooth four-manifolds},
JOURNAL = {Adv. Math.},
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} -
[OSzKnotInv]
P. Ozsváth and Z. Szabó, "Holomorphic disks and knot invariants," Adv. Math., vol. 186, iss. 1, pp. 58-116, 2004.
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AUTHOR = {Ozsv{á}th, Peter and Szab{ó},
Zolt{á}n},
TITLE = {Holomorphic disks and knot invariants},
JOURNAL = {Adv. Math.},
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NUMBER = {1},
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CODEN = {ADMTA4},
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MRREVIEWER = {Stanislav Jabuka},
DOI = {10.1016/j.aim.2003.05.001},
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} -
[OSzGenusBound]
P. Ozsváth and Z. Szabó, "Holomorphic disks and genus bounds," Geom. Topol., vol. 8, pp. 311-334, 2004.
@article {OSzGenusBound, MRKEY = {2023281},
AUTHOR = {Ozsv{á}th, Peter and Szab{ó},
Zolt{á}n},
TITLE = {Holomorphic disks and genus bounds},
JOURNAL = {Geom. Topol.},
FJOURNAL = {Geometry and Topology},
VOLUME = {8},
YEAR = {2004},
PAGES = {311--334},
ISSN = {1465-3060},
MRCLASS = {57M27 (53D35 57N10 57R58)},
MRNUMBER = {2004m:57024},
MRREVIEWER = {Jacob Andrew Rasmussen},
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} -
[OSz4BallGenus]
P. Ozsváth and Z. Szabó, "Knot Floer homology and the four-ball genus," Geom. Topol., vol. 7, pp. 615-639, 2003.
@article {OSz4BallGenus, MRKEY = {2026543},
AUTHOR = {Ozsv{á}th, Peter and Szab{ó},
Zolt{á}n},
TITLE = {Knot {F}loer homology and the four-ball genus},
JOURNAL = {Geom. Topol.},
FJOURNAL = {Geometry and Topology},
VOLUME = {7},
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PAGES = {615--639},
ISSN = {1465-3060},
MRCLASS = {57R58 (57M25 57M27)},
MRNUMBER = {2004i:57036},
MRREVIEWER = {Stanislav Jabuka},
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} -
[OSzLinkInv] P. Ozsváth and Z. Szabó, "Holomorphic disks, link invariants and the multi-variable Alexander polynomial," Algebr. Geom. Topol., vol. 8, pp. 615-692, 2008.
@article{OSzLinkInv,
author={Ozsv{á}th, Peter and Szab{ó},
Zolt{á}n},
TITLE={Holomorphic disks, link invariants and the multi-variable Alexander polynomial},
JOURNAL={Algebr. Geom. Topol.},
VOLUME={8},
YEAR={2008},
PAGES={615--692},
MRNUMBER={2443092},
ZBLNUMBER={1144.57011},
} -
[OSzThurstonNorm]
P. Ozsváth and Z. Szabó, "Link Floer homology and the Thurston norm," J. Amer. Math. Soc., vol. 21, iss. 3, pp. 671-709, 2008.
@article {OSzThurstonNorm, MRKEY = {2393424},
AUTHOR = {Ozsv{á}th, Peter and Szab{ó},
Zolt{á}n},
TITLE = {Link {F}loer homology and the {T}hurston norm},
JOURNAL = {J. Amer. Math. Soc.},
FJOURNAL = {Journal of the American Mathematical Society},
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NUMBER = {3},
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MRCLASS = {57R58 (57M27)},
MRNUMBER = {2009a:57050},
MRREVIEWER = {Stanislav Jabuka},
DOI = {10.1090/S0894-0347-08-00586-9},
} -
[OSzICMTalk] P. Ozsváth and Z. Szabó, "Heegaard diagrams and Floer homology," in International Congress of Mathematicians. Vol. II, Eur. Math. Soc., Zürich, 2006, pp. 1083-1099.
@incollection {OSzICMTalk, MRKEY = {2275636},
AUTHOR = {Ozsv{á}th, Peter and Szab{ó},
Zolt{á}n},
TITLE = {Heegaard diagrams and {F}loer homology},
BOOKTITLE = {International {C}ongress of {M}athematicians. {V}ol. {\rm II}},
PAGES = {1083--1099},
PUBLISHER = {Eur. Math. Soc., Zürich},
YEAR = {2006},
MRCLASS = {57R58 (57M27)},
MRNUMBER = {2008h:57048},
MRREVIEWER = {Thomas E. Mark},
} -
[Differentfaces] P. Ozsváth and Z. Szabó, "Heegaard diagrams and holomorphic disks," in Different Faces of Geometry, New York: Kluwer/Plenum, 2004, pp. 301-348.
@incollection {Differentfaces, MRKEY = {2102999},
AUTHOR = {Ozsv{á}th, Peter and Szab{ó},
Zolt{á}n},
TITLE = {Heegaard diagrams and holomorphic disks},
BOOKTITLE = {Different Faces of Geometry},
SERIES = {Int. Math. Ser.},
NUMBER = {3},
PAGES = {301--348},
PUBLISHER = {Kluwer/Plenum},
ADDRESS={New York},
YEAR = {2004},
MRCLASS = {57R58 (32Q65 57M27 57R17)},
MRNUMBER = {2005g:57057},
MRREVIEWER = {Thomas E. Mark},
ZBLNUMBER = {1091.57010},
} -
[Rasmussen] J. Rasmussen, "Floer homology and knot complements," PhD Thesis , Harvard University, 2003.
@phdthesis{Rasmussen,
author={Rasmussen, J.},
TITLE={Floer homology and knot complements},
SCHOOl={Harvard University},
YEAR={2003},
}