Induced quasi-actions: A remark

Kleiner, Bruce; Leeb, Bernhard

doi:10.1090/S0002-9939-08-09742-6

Induced quasi-actions: A remark
HTML articles powered by AMS MathViewer

by Bruce Kleiner and Bernhard Leeb PDF

Proc. Amer. Math. Soc. 137 (2009), 1561-1567 Request permission

Abstract:

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

References

A. Reiter 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, DOI 10.1023/A:1019630514124
M. Bonk, B. Kleiner, and S. Merenkov, Rigidity of Schottky sets, Amer. J. Math., to appear.
Marc Bourdon and Hervé Pajot, Rigidity of quasi-isometries for some hyperbolic buildings, Comment. Math. Helv. 75 (2000), no. 4, 701–736. MR 1789183, DOI 10.1007/s000140050146
Richard Chow, Groups quasi-isometric to complex hyperbolic space, Trans. Amer. Math. Soc. 348 (1996), no. 5, 1757–1769. MR 1329530, DOI 10.1090/S0002-9947-96-01522-X
Andrew Casson and Douglas Jungreis, Convergence groups and Seifert fibered $3$-manifolds, Invent. Math. 118 (1994), no. 3, 441–456. MR 1296353, DOI 10.1007/BF01231540
David Gabai, Convergence groups are Fuchsian groups, Ann. of Math. (2) 136 (1992), no. 3, 447–510. MR 1189862, DOI 10.2307/2946597
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, N.J., 1981, pp. 183–213. MR 624814
A. Hinkkanen, Abelian and nondiscrete convergence groups on the circle, Trans. Amer. Math. Soc. 318 (1990), no. 1, 87–121. MR 1000145, DOI 10.1090/S0002-9947-1990-1000145-X
Michael Kapovich, Bruce Kleiner, and Bernhard Leeb, Quasi-isometries and the de Rham decomposition, Topology 37 (1998), no. 6, 1193–1211. MR 1632904, DOI 10.1016/S0040-9383(97)00091-8
M. Kapovich, B. Kleiner, B. Leeb, and R. Schwartz, private communication.
Bruce Kleiner and Bernhard Leeb, Rigidity of quasi-isometries for symmetric spaces and Euclidean buildings, Inst. Hautes Études Sci. Publ. Math. 86 (1997), 115–197 (1998). MR 1608566, DOI 10.1007/BF02698902
Bruce Kleiner and Bernhard Leeb, Groups quasi-isometric to symmetric spaces, Comm. Anal. Geom. 9 (2001), no. 2, 239–260. MR 1846203, DOI 10.4310/CAG.2001.v9.n2.a1
Bernhard Leeb, A characterization of irreducible symmetric spaces and Euclidean buildings of higher rank by their asymptotic geometry, Bonner Mathematische Schriften [Bonn Mathematical Publications], vol. 326, Universität Bonn, Mathematisches Institut, Bonn, 2000. MR 1934160
Vladimir Markovic, Quasisymmetric groups, J. Amer. Math. Soc. 19 (2006), no. 3, 673–715. MR 2220103, DOI 10.1090/S0894-0347-06-00518-2
G. D. Mostow, Strong rigidity of locally symmetric spaces, Annals of Mathematics Studies, No. 78, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1973. MR 0385004
Lee Mosher, Michah Sageev, and Kevin Whyte, Quasi-actions on trees. I. Bounded valence, Ann. of Math. (2) 158 (2003), no. 1, 115–164. MR 1998479, DOI 10.4007/annals.2003.158.115
Pierre Pansu, Métriques de Carnot-Carathéodory et quasiisométries des espaces symétriques de rang un, Ann. of Math. (2) 129 (1989), no. 1, 1–60 (French, with English summary). MR 979599, DOI 10.2307/1971484
Dennis 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, N.Y., 1978) Ann. of Math. Stud., vol. 97, Princeton Univ. Press, Princeton, N.J., 1981, pp. 465–496. MR 624833
Pekka Tukia, On quasiconformal groups, J. Analyse Math. 46 (1986), 318–346. MR 861709, DOI 10.1007/BF02796595
Xiangdong Xie, Quasi-isometric rigidity of Fuchsian buildings, Topology 45 (2006), no. 1, 101–169. MR 2170496, DOI 10.1016/j.top.2005.06.005