Abstract
Let $\mathbf{M}^3$ be a closed hyperbolic three manifold. We construct closed surfaces that map by immersions into $\mathbf{M}^3$ so that for each, one the corresponding mapping on the universal covering spaces is an embedding, or, in other words, the corresponding induced mapping on fundamental groups is an injection.
-
[bowen] L. Bowen, Weak Forms of the Ehrenpreis conjecture and the surface subgroup conjecture.
@misc{bowen,
author={Bowen, L.},
TITLE={Weak Forms of the {E}hrenpreis conjecture and the surface subgroup conjecture},
ARXIV={math/0411662},
} -
[brin-gromov]
M. Brin and M. Gromov, "On the ergodicity of frame flows," Invent. Math., vol. 60, iss. 1, pp. 1-7, 1980.
@article {brin-gromov, MRKEY = {0582702},
AUTHOR = {Brin, M. and Gromov, M.},
TITLE = {On the ergodicity of frame flows},
JOURNAL = {Invent. Math.},
FJOURNAL = {Inventiones Mathematicae},
VOLUME = {60},
YEAR = {1980},
NUMBER = {1},
PAGES = {1--7},
ISSN = {0020-9910},
CODEN = {INVMBH},
MRCLASS = {58F17 (58F11)},
MRNUMBER = {0582702},
MRREVIEWER = {Gudlaugur Thorbergsson},
DOI = {10.1007/BF01389897},
ZBLNUMBER = {0445.58023},
} -
[calegari] D. Calegari, SCL, Tokyo: Math. Soc. Japan, 2009, vol. 20.
@book {calegari, MRKEY = {2527432},
AUTHOR = {Calegari, Danny},
TITLE = {{SCL}},
SERIES = {MSJ Memoirs},
VOLUME = {20},
PUBLISHER = {Math. Soc. Japan},
ADDRESS = {Tokyo},
YEAR = {2009},
PAGES = {xii+209},
ISBN = {978-4-931469-53-2},
MRCLASS = {57M07 (20F65 20F67 20J05 37E45)},
MRNUMBER = {2527432},
MRREVIEWER = {Athanase Papadopoulos},
ZBLNUMBER = {1187.20035},
} -
[epstein] R. D. Canary, D. B. A. Epstein, and P. L. Green, "Notes on notes of Thurston [MR0903850]," in Fundamentals of Hyperbolic Geometry: Selected Expositions, Cambridge: Cambridge Univ. Press, 2006, vol. 328, pp. 1-115.
@incollection {epstein, MRKEY = {2235710},
AUTHOR = {Canary, R. D. and Epstein, D. B. A. and Green, P. L.},
TITLE = {Notes on notes of {T}hurston [{MR}0903850]},
BOOKTITLE = {Fundamentals of Hyperbolic Geometry: Selected Expositions},
SERIES = {London Math. Soc. Lecture Note Ser.},
VOLUME = {328},
PAGES = {1--115},
NOTE = {With a new foreword by Canary},
PUBLISHER = {Cambridge Univ. Press},
ADDRESS = {Cambridge},
YEAR = {2006},
MRCLASS = {57N10 (32G15 37D40 37F99 54A20 57M99)},
MRNUMBER = {2235710},
ZBLNUMBER = {0612.57009},
} -
[c-l-r]
D. Cooper, D. D. Long, and A. W. Reid, "Essential closed surfaces in bounded $3$-manifolds," J. Amer. Math. Soc., vol. 10, iss. 3, pp. 553-563, 1997.
@article {c-l-r, MRKEY = {1431827},
AUTHOR = {Cooper, D. and Long, D. D. and Reid, A. W.},
TITLE = {Essential closed surfaces in bounded {$3$}-manifolds},
JOURNAL = {J. Amer. Math. Soc.},
FJOURNAL = {Journal of the American Mathematical Society},
VOLUME = {10},
YEAR = {1997},
NUMBER = {3},
PAGES = {553--563},
ISSN = {0894-0347},
MRCLASS = {57N10 (57M05 57M10 57N35)},
MRNUMBER = {1431827},
MRREVIEWER = {Darryl McCullough},
DOI = {10.1090/S0894-0347-97-00236-1},
ZBLNUMBER = {0896.57009},
} -
[fletcher-markovic] A. Fletcher and V. Markovic, Quasiconformal Maps and Teichmüller Theory, Oxford: Oxford University Press, 2007, vol. 11.
@book {fletcher-markovic, MRKEY = {2269887},
AUTHOR = {Fletcher, A. and Markovic, V.},
TITLE = {Quasiconformal Maps and {T}eichmüller Theory},
SERIES = {Oxford Grad. Texts Math.},
VOLUME = {11},
PUBLISHER = {Oxford University Press},
ADDRESS = {Oxford},
YEAR = {2007},
PAGES = {viii+189},
ISBN = {978-0-19-856926-8; 0-19-856926-2},
MRCLASS = {30-01 (30C62 32G15)},
MRNUMBER = {2269887},
ZBLNUMBER = {1103.30002},
} -
[kour]
C. Kourouniotis, "Complex length coordinates for quasi-Fuchsian groups," Mathematika, vol. 41, iss. 1, pp. 173-188, 1994.
@article {kour, MRKEY = {1288062},
AUTHOR = {Kourouniotis, Christos},
TITLE = {Complex length coordinates for quasi-{F}uchsian groups},
JOURNAL = {Mathematika},
FJOURNAL = {Mathematika. A Journal of Pure and Applied Mathematics},
VOLUME = {41},
YEAR = {1994},
NUMBER = {1},
PAGES = {173--188},
ISSN = {0025-5793},
CODEN = {MTKAAB},
MRCLASS = {30F40 (20H10 30F35 30F60)},
MRNUMBER = {1288062},
DOI = {10.1112/S0025579300007270},
ZBLNUMBER = {0801.30036},
} -
[kahn-markovic] J. Kahn and V. Markovic, The Weil-Petersson distance between finite degree covers of punctured Riemann surfaces and random ideal triangulations.
@misc{kahn-markovic,
author={Kahn, J. and Markovic, V.},
TITLE={The {W}eil-{P}etersson distance between finite degree covers of punctured {R}iemann surfaces and random ideal triangulations},
ARXIV={0806.2304},
} -
[lackenby]
M. Lackenby, "Surface subgroups of Kleinian groups with torsion," Invent. Math., vol. 179, iss. 1, pp. 175-190, 2010.
@article {lackenby, MRKEY = {2563763},
AUTHOR = {Lackenby, Marc},
TITLE = {Surface subgroups of {K}leinian groups with torsion},
JOURNAL = {Invent. Math.},
FJOURNAL = {Inventiones Mathematicae},
VOLUME = {179},
YEAR = {2010},
NUMBER = {1},
PAGES = {175--190},
ISSN = {0020-9910},
CODEN = {INVMBH},
MRCLASS = {30F40 (20H10)},
MRNUMBER = {2563763},
MRREVIEWER = {Jane Gilman},
DOI = {10.1007/s00222-009-0215-5},
ZBLNUMBER = {1183.57017},
} -
[moore] C. C. Moore, "Exponential decay of correlation coefficients for geodesic flows," in Group Representations, Ergodic Theory, Operator Algebras, and Mathematical Physics, New York: Springer-Verlag, 1987, vol. 163–181.
@incollection {moore, MRKEY = {0880376},
AUTHOR = {Moore, Calvin C.},
TITLE = {Exponential decay of correlation coefficients for geodesic flows},
BOOKTITLE = {Group Representations, Ergodic Theory, Operator Algebras, and Mathematical Physics},
VENUE={{B}erkeley, {C}alif., 1984},
SERIES = {Math. Sci. Res. Inst. Publ.},
NUMBER = {6},
VOLUME = {163--181},
PUBLISHER = {Springer-Verlag},
ADDRESS = {New York},
YEAR = {1987},
MRCLASS = {58F17 (22E45)},
MRNUMBER = {0880376},
ZBLNUMBER = {0625.58023},
} -
[pollicott]
M. Pollicott, "Exponential mixing for the geodesic flow on hyperbolic three-manifolds," J. Statist. Phys., vol. 67, iss. 3-4, pp. 667-673, 1992.
@article {pollicott, MRKEY = {1171148},
AUTHOR = {Pollicott, Mark},
TITLE = {Exponential mixing for the geodesic flow on hyperbolic three-manifolds},
JOURNAL = {J. Statist. Phys.},
FJOURNAL = {Journal of Statistical Physics},
VOLUME = {67},
YEAR = {1992},
NUMBER = {3-4},
PAGES = {667--673},
ISSN = {0022-4715},
CODEN = {JSTPSB},
MRCLASS = {58F17 (22E40)},
MRNUMBER = {1171148},
MRREVIEWER = {Alexander Starkov},
DOI = {10.1007/BF01049724},
ZBLNUMBER = {0892.58060},
} -
[ser-tan]
S. P. Tan, "Complex Fenchel-Nielsen coordinates for quasi-Fuchsian structures," Internat. J. Math., vol. 5, iss. 2, pp. 239-251, 1994.
@article {ser-tan, MRKEY = {1266284},
AUTHOR = {Tan, Ser Peow},
TITLE = {Complex {F}enchel-{N}ielsen coordinates for quasi-{F}uchsian structures},
JOURNAL = {Internat. J. Math.},
FJOURNAL = {International Journal of Mathematics},
VOLUME = {5},
YEAR = {1994},
NUMBER = {2},
PAGES = {239--251},
ISSN = {0129-167X},
MRCLASS = {32G15 (57M50)},
MRNUMBER = {1266284},
MRREVIEWER = {Takayuki Okai},
DOI = {10.1142/S0129167X94000140},
ZBLNUMBER = {0816.32017},
} -
[series]
C. Series, "An extension of Wolpert’s derivative formula," Pacific J. Math., vol. 197, iss. 1, pp. 223-239, 2001.
@article {series, MRKEY = {1810217},
AUTHOR = {Series, Caroline},
TITLE = {An extension of {W}olpert's derivative formula},
JOURNAL = {Pacific J. Math.},
FJOURNAL = {Pacific Journal of Mathematics},
VOLUME = {197},
YEAR = {2001},
NUMBER = {1},
PAGES = {223--239},
ISSN = {0030-8730},
CODEN = {PJMAAI},
MRCLASS = {30F40 (20H10 57M50)},
MRNUMBER = {1810217},
MRREVIEWER = {Fr{é}d{é}ric Paulin},
ZBLNUMBER = {1065.30044},
DOI = {10.2140/pjm.2001.197.223},
}