Dimension and rank for mapping class groups

Annals of Mathematics

Volumn 167, Issue 3, 2008, Pages 1055-1077

  Behrstock, Jason A ^a   Minsky, Yair N ^b  

^a UNIVERSITY OF UTAH   (United States)

^b YALE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 49749143298     PISSN: 0003486X     EISSN: None     Source Type: Journal    
DOI: 10.4007/annals.2008.167.1055     Document Type: Article

References (23)

1. J. ARAMAYONA, The Weil-Petersson geometry of the five-times punctured sphere, in Spaces of Kleinian Groups, 219-231, London Math. Soc. Lecture Notes Ser. 329, Cambridge Univ. Press, Cambridge, 2006, Ph.D. thesis, University of Southampton, U.K., May 2004.
2. J. BEHRSTOCK, Asymptotic geometry of the mapping class group and Teichmüller space, Geometry & Topology 10 (2006) 1523-1578.
3. J. BIRMAN, Braids, Links, and Mapping Class Groups, Annals of Math. Studies 82, Princeton Univ. Press, Princeton, NJ, 1974.
4. J. BIRMAN, A. LUBOTZKY, and J. MCC ARTHY, Abelian and solvable subgroups of the mapping class groups, Duke Math. J. 50 (1983), 1107-1120.
5. B. BOWDITCH, Intersection numbers and the hyperbolicity of the curve complex, J. Reine Angew. Math. 598 (2006), 105-129.
6. J. BROCK, The Weil-Petersson metric and volumes of 3-dimensional hyperbolic convex cores, J. Amer. Math. Soc. 16 (2003), 495-535 (electronic).
7. J. BROCK and B. FARB, Curvature and rank of Teichmüller space, American J. Math. 128 (2006), 1-22.
8. J. BROCK and H. MASUR, Quasi-geodesics and relative hyperbolicity in the pants complex, in preparation.
9. J. BURILLO, Dimension and fundamental groups of asymptotic cones, J. London Math. Soc. 59 (1999), 557-572.
10. M. DEHN, Papers on Group Theory and Topology, Springer-Verlag, New York, 1987, translated from the German and with introductions and an appendix by John Stillwell, with an appendix by Otto Schreier.
11. L. VAN DEN DRIES and A. WILKIE, Gromov's theorem on groups of polynomial growth and elementary logic, J. Algebra 89 (1984), 349-374.
12. C. DRUŢU and M. SAPIR, Tree-graded spaces and asymptotic cones of groups, Topology 44 (2005), 959-1058, with an appendix by Denis Osin and Mark Sapir.
13. R. ENGELKING, General Topology, Sigma Series in Pure Math. 6, second edition, Heldermann Verlag, Berlin, 1989, translated from the Polish by the author.
14. _, Theory of Dimensions Finite and Infinite, Sigma Series in Pure Math. 10, Heldermann Verlag, Lemgo, 1995.
15. B. FARB, A. LUBOTZKY, and Y. MINSKY, Rank-1 phenomena for mapping class groups, Duke Math. J. 106 (2001), 581-597.
16. M. GROMOV, Groups of polynomial growth and expanding maps, IHES Sci. Publ. Math. 53 (1981), 53-73.
17. _, Infinite groups as geometric objects, in Proc. of the International Congress of Mathematicians, Warsaw, 385-392, Amer. Math. Soc., Providence, RI, 1983.
18. U. HAMENSTÄDT, Geometry of the mapping class groups III: Quasi-isometric rigidity, Preprint; arXiv:math.GT/0512429.
19. M. KAPOVICH and B. LEEB, Quasi-isometries preserve the geometric decomposition of Haken manifolds, Invent. Math. 128 (1997), 393-416.
20. B. KLEINER and B. LEEB, Rigidity of quasi-isometries for symmetric spaces and Euclidean buildings, IHES Publ. Math. 86 (1997), 115-197.
21. H. MASUR and Y. MINSKY, Geometry of the complex of curves, I. Hyperbolicity, Invent. Math. 138 (1999), 103-149.
22. _, Geometry of the complex of curves II: Hierarchical structure, Geom. Funct. Anal. 10 (2000), 902-974.
23. L. MOSHER, Mapping class groups are automatic, Ann. of Math. 142 (1995), 303-384.