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  • Séminaire de théorie spectrale et géométrie
  • Tome 28 (2009-2010)
  • p. 63-107
  • Suivant
Cannon-Thurston Maps, i-bounded Geometry and a Theorem of McMullen
Mahan Mj1
1 RKM Vivekananda University School of Mathematical Sciences P.O. Belur Math Dt. Howrah, WB-711202 (India)
Séminaire de théorie spectrale et géométrie, Tome 28 (2009-2010), pp. 63-107.
  • Résumé

The notion of i-bounded geometry generalises simultaneously bounded geometry and the geometry of punctured torus Kleinian groups. We show that the limit set of a surface Kleinian group of i-bounded geometry is locally connected by constructing a natural Cannon-Thurston map.

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DOI : 10.5802/tsg.279
Classification : 57M50
Affiliations des auteurs :
Mahan Mj 1

1 RKM Vivekananda University School of Mathematical Sciences P.O. Belur Math Dt. Howrah, WB-711202 (India)
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@article{TSG_2009-2010__28__63_0,
     author = {Mahan Mj},
     title = {Cannon-Thurston {Maps,} i-bounded {Geometry} and a {Theorem} of {McMullen}},
     journal = {S\'eminaire de th\'eorie spectrale et g\'eom\'etrie},
     pages = {63--107},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {28},
     year = {2009-2010},
     doi = {10.5802/tsg.279},
     language = {en},
     url = {https://proceedings.centre-mersenne.org/articles/10.5802/tsg.279/}
}
TY  - JOUR
AU  - Mahan Mj
TI  - Cannon-Thurston Maps, i-bounded Geometry and a Theorem of McMullen
JO  - Séminaire de théorie spectrale et géométrie
PY  - 2009-2010
SP  - 63
EP  - 107
VL  - 28
PB  - Institut Fourier
PP  - Grenoble
UR  - https://proceedings.centre-mersenne.org/articles/10.5802/tsg.279/
DO  - 10.5802/tsg.279
LA  - en
ID  - TSG_2009-2010__28__63_0
ER  - 
%0 Journal Article
%A Mahan Mj
%T Cannon-Thurston Maps, i-bounded Geometry and a Theorem of McMullen
%J Séminaire de théorie spectrale et géométrie
%D 2009-2010
%P 63-107
%V 28
%I Institut Fourier
%C Grenoble
%U https://proceedings.centre-mersenne.org/articles/10.5802/tsg.279/
%R 10.5802/tsg.279
%G en
%F TSG_2009-2010__28__63_0
Mahan Mj. Cannon-Thurston Maps, i-bounded Geometry and a Theorem of McMullen. Séminaire de théorie spectrale et géométrie, Tome 28 (2009-2010), pp. 63-107. doi : 10.5802/tsg.279. https://proceedings.centre-mersenne.org/articles/10.5802/tsg.279/
  • Bibliographie
  • Cité par

[1] Brian H. Bowditch Relatively hyperbolic groups (preprint, Southampton, 1997)

[2] Brian H. Bowditch The Cannon-Thurston map for punctured-surface groups, Math. Z., Volume 255 (2007) no. 1, pp. 35-76 | MR | Zbl

[3] James W. Cannon; William P. Thurston Group invariant Peano curves, Geom. Topol., Volume 11 (2007), pp. 1315-1355 | MR | Zbl

[4] M. Coornaert; T. Delzant; A. Papadopoulos Géométrie et théorie des groupes, Lecture Notes in Mathematics, 1441, Springer-Verlag, Berlin, 1990 (Les groupes hyperboliques de Gromov. [Gromov hyperbolic groups], With an English summary) | MR | Zbl

[5] Shubhabrata Das; Mahan Mj Addendum to Ending Laminations and Cannon-Thurston Maps: Parabolics (arXiv:1002.2090, 2010)

[6] Shubhabrata Das; Mahan Mj Semiconjugacies Between Relatively Hyperbolic Boundaries (arXiv:1007.2547, 2010)

[7] B. Farb Relatively hyperbolic groups, Geom. Funct. Anal., Volume 8 (1998) no. 5, pp. 810-840 | MR | Zbl

[8] Étienne Ghys; Pierre de la Harpe La propriété de Markov pour les groupes hyperboliques, Sur les groupes hyperboliques d’après Mikhael Gromov (Bern, 1988) (Progr. Math.), Volume 83, Birkhäuser Boston, Boston, MA, 1990, pp. 165-187

[9] M. Gromov Hyperbolic groups, Essays in group theory (Math. Sci. Res. Inst. Publ.), Volume 8, Springer, New York, 1987, pp. 75-263 | MR | Zbl

[10] M. Gromov Asymptotic invariants of infinite groups, Geometric group theory, Vol. 2 (Sussex, 1991) (London Math. Soc. Lecture Note Ser.), Volume 182, Cambridge Univ. Press, Cambridge, 1993, pp. 1-295 | MR

[11] John G. Hocking; Gail S. Young Topology, Addison-Wesley Publishing Co., Inc., Reading, Mass.-London, 1961 | MR

[12] Erica Klarreich Semiconjugacies between Kleinian group actions on the Riemann sphere, Amer. J. Math., Volume 121 (1999) no. 5, pp. 1031-1078 | MR | Zbl

[13] Curtis T. McMullen Local connectivity, Kleinian groups and geodesics on the blowup of the torus, Invent. Math., Volume 146 (2001) no. 1, pp. 35-91 | MR | Zbl

[14] Yair Minsky The classification of Kleinian surface groups. I. Models and bounds, Ann. of Math. (2), Volume 171 (2010) no. 1, pp. 1-107 | MR | Zbl

[15] Yair N. Minsky On rigidity, limit sets, and end invariants of hyperbolic 3-manifolds, J. Amer. Math. Soc., Volume 7 (1994) no. 3, pp. 539-588 | MR | Zbl

[16] Yair N. Minsky The classification of punctured-torus groups, Ann. of Math. (2), Volume 149 (1999) no. 2, pp. 559-626 | MR | Zbl

[17] Mahan Mitra Cannon-Thurston maps for hyperbolic group extensions, Topology, Volume 37 (1998) no. 3, pp. 527-538 | MR | Zbl

[18] Mahan Mitra Cannon-Thurston maps for trees of hyperbolic metric spaces, J. Differential Geom., Volume 48 (1998) no. 1, pp. 135-164 | MR | Zbl

[19] Mahan Mj Cannon-Thurston Maps for Kleinian Groups (preprint, arXiv:math 1002.0996, 2010) | MR

[20] Mahan Mj Cannon-Thurston Maps for Surface Groups (preprint, arXiv:math.GT/0607509, 2006) | MR

[21] Mahan Mj Cannon-Thurston Maps for Surface Groups (preprint, arXiv:math.GT/0512539, 2005) | MR

[22] Mahan Mj Ending Laminations and Cannon-Thurston Maps (submitted, arXiv:math.GT/0702162, 2007) | MR

[23] Mahan Mj Cannon-Thurston maps for pared manifolds of bounded geometry, Geom. Topol., Volume 13 (2009) no. 1, pp. 189-245 | MR | Zbl

[24] Mahan Mj Cannon-Thurston maps and bounded geometry, Teichmüller theory and moduli problem (Ramanujan Math. Soc. Lect. Notes Ser.), Volume 10, Ramanujan Math. Soc., Mysore, 2010, pp. 489-511 | MR | Zbl

[25] William P. Thurston Three-dimensional geometry and topology. Vol. 1, Princeton Mathematical Series, 35, Princeton University Press, Princeton, NJ, 1997 (Edited by Silvio Levy) | MR | Zbl

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