Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Induced quasi-actions: A remark

Authors: Bruce Kleiner and Bernhard Leeb
Journal: Proc. Amer. Math. Soc. 137 (2009), 1561-1567
MSC (2000): Primary 20F65
Published electronically: November 13, 2008
MathSciNet review: 2470813
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We observe that the notion of an induced representation has an analog for quasi-actions and give some applications.

References [Enhancements On Off] (What's this?)

  • [Ahl02] A. R. Ahlin, The large scale geometry of products of trees, Geom. Dedicata 92 (2002), 179-184, Dedicated to John Stallings on the occasion of his 65th birthday. MR 1934017 (2003j:20041)
  • [BKM] M. Bonk, B. Kleiner, and S. Merenkov, Rigidity of Schottky sets, Amer. J. Math., to appear.
  • [BP00] M. Bourdon and H. Pajot, Rigidity of quasi-isometries for some hyperbolic buildings, Comment. Math. Helv. 75 (2000), no. 4, 701-736. MR 1789183 (2003a:30027)
  • [Cho96] R. Chow, Groups quasi-isometric to complex hyperbolic space, Trans. Amer. Math. Soc. 348 (1996), no. 5, 1757-1769. MR 1329530 (96h:20071)
  • [CJ94] A. Casson and D. Jungreis, Convergence groups and Seifert fibered $ 3$-manifolds, Invent. Math. 118 (1994), no. 3, 441-456. MR 1296353 (96f:57011)
  • [Gab92] D. Gabai, Convergence groups are Fuchsian groups, Ann. of Math. (2) 136 (1992), no. 3, 447-510. MR 1189862 (93m:20065)
  • [Gro] M. Gromov, Hyperbolic manifolds, groups and actions, Riemann surfaces and related topics: Proceedings of the 1978 Stony Brook Conference (State Univ. New York, Stony Brook, N.Y., 1978), Ann. of Math. Stud., vol. 97, Princeton Univ. Press, Princeton, NJ, 1981, pp. 183-213. MR 624814 (82m:53035)
  • [Hin90] A. Hinkkanen, Abelian and nondiscrete convergence groups on the circle, Trans. Amer. Math. Soc. 318 (1990), no. 1, 87-121. MR 1000145 (91g:30025)
  • [KKL98] M. Kapovich, B. Kleiner, and B. Leeb, Quasi-isometries and the de Rham decomposition, Topology 37 (1998), no. 6, 1193-1211. MR 1632904 (99g:53048)
  • [KKLS] M. Kapovich, B. Kleiner, B. Leeb, and R. Schwartz, private communication.
  • [KL97] B. Kleiner and B. Leeb, Rigidity of quasi-isometries for symmetric spaces and Euclidean buildings, Inst. Hautes Études Sci. Publ. Math. (1997), no. 86, 115-197 (1998). MR 1608566 (98m:53068)
  • [KL01] -, Groups quasi-isometric to symmetric spaces, Comm. Anal. Geom. 9 (2001), no. 2, 239-260. MR 1846203 (2002d:53066)
  • [Lee00] B. Leeb, A characterization of irreducible symmetric spaces and Euclidean buildings of higher rank by their asymptotic geometry, Bonner Mathematische Schriften [Bonn Mathematical Publications], 326, Universität Bonn Mathematisches Institut, Bonn, 2000. MR 1934160 (2004b:53060)
  • [Mar06] V. Markovic, Quasisymmetric groups, J. Amer. Math. Soc. 19 (2006), no. 3, 673-715 (electronic). MR 2220103 (2007c:37057)
  • [Mos73] G. D. Mostow, Strong rigidity of locally symmetric spaces, Ann. Math. Stud., vol. 78, Princeton University Press, Princeton, NJ; University of Tokyo Press, Tokyo, 1973. MR 0385004 (52:5874)
  • [MSW03] L. Mosher, M. Sageev, and K. Whyte, Quasi-actions on trees. I. Bounded valence, Ann. of Math. (2) 158 (2003), no. 1, 115-164. MR 1998479 (2004h:20055)
  • [Pan89] P. Pansu, Métriques de Carnot-Carathéodory et quasiisométries des espaces symétriques de rang un, Ann. of Math. (2) 129 (1989), no. 1, 1-60. MR 979599 (90e:53058)
  • [Sul81] D. Sullivan, On the ergodic theory at infinity of an arbitrary discrete group of hyperbolic motions, Riemann surfaces and related topics: Proceedings of the 1978 Stony Brook Conference (State Univ. New York, Stony Brook, NY, 1978), Ann. of Math. Stud., vol. 97, Princeton Univ. Press, Princeton, NJ, 1981, pp. 465-496. MR 624833 (83f:58052)
  • [Tuk86] P. Tukia, On quasiconformal groups, J. Analyse Math. 46 (1986), 318-346. MR 861709 (87m:30043)
  • [Xie06] X. Xie, Quasi-isometric rigidity of Fuchsian buildings, Topology 45 (2006), no. 1, 101-169. MR 2170496 (2006m:53064)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 20F65

Retrieve articles in all journals with MSC (2000): 20F65

Additional Information

Bruce Kleiner
Affiliation: Department of Mathematics, Yale University, New Haven, Connecticut 06520
Address at time of publication: Courant Institute of Mathematical Sciences, 251 Mercer Street, New York, New York 10012-1185

Bernhard Leeb
Affiliation: Mathematisches Institut, Universität München, Theresienstr. 39, D-80333 München, Germany

Received by editor(s): February 25, 2008
Received by editor(s) in revised form: June 23, 2008
Published electronically: November 13, 2008
Additional Notes: The first author was partially supported by NSF Grant DMS 0701515
Communicated by: Alexander N. Dranishnikov
Article copyright: © Copyright 2008 American Mathematical Society

American Mathematical Society