Representations of fundamental groups of manifolds with a semisimple transformation group

Robert J. Zimmer

Type: Article

Publication Date: 1989-01-01

Citations: 36

DOI: https://doi.org/10.1090/s0894-0347-1989-0973308-2

Abstract

group ? 1 (M) , and the Lie groups that can act on M. More precisely, let G be a connected semisimple Lie group of higher real rank, and suppose G acts continuously on a (topological) manifold M, preserving a finite measure. The main theme of this paper is that the representation theory of 7r I(M) in low dimensions is to a large extent controlled by that of G (the latter of course being well understood). In particular, under natural hypotheses (e.g., that the action of G on M is engaging, i.e., there is no loss of ergodicity in passing to finite covers; see Definition 3.1 below), we prove that if G has no nontrivial

Locations

Journal of the American Mathematical Society - View - PDF

Similar Works

Action	Title	Year	Authors
+ PDF Chat	Semisimple automorphism groups of $G$-structures	1984	Robert J. Zimmer
+ PDF Chat	Representations of Fundamental Groups of Manifolds with a Semisimple Transformation Group	1989	Robert J. Zimmer
+ PDF Chat	Fundamental Groups of Semisimple Symmetric Spaces	2018	Jiro Sekiguchi
+ PDF Chat	Rigidity of ergodic volume-preserving actions of semisimple groups of higher rank on compact manifolds	1994	Guillaume Seydoux
+ PDF Chat	Fundamental Groups of Semisimple Symmetric Spaces	1988	Jiro Sekiguchi
+ PDF Chat	Fundamental Groups of Semisimple Symmetric Spaces, II	1996	Jiro Sekiguchi
+ PDF Chat	Rigidity of Ergodic Volume-Preserving Actions of Semisimple Groups of Higher Rank on Compact Manifolds	1994	Guillaume Seydoux
+	Finite-Dimensional Representations of Lie Groups	1986
+	Representations of Compact Groups	2000	J. J. Duistermaat J. A. C. Kolk
+ PDF Chat	Fundamental groups of compact manifolds and symmetric geometry of noncompact type	1999	Alberto Candel Raúl Quiroga-Barranco
+	Invariant deformations of orbit closures in $\mathfrak{sl}_n$	2007	Sébastien Jansou Nicolas Ressayre
+ PDF Chat	Representations of Compact Lie Groups	2007
+	Representations of Compact Lie Groups	1997	Krzysztof Maurin
+ PDF Chat	Representations of Compact Lie Groups	1999
+	Representations of Compact Lie Groups	1985	Theodor Bröcker Tammo tom Dieck
+	Ergodic Theory and Semisimple Groups	1984	Robert J. Zimmer
+	On low-dimensional manifolds with isometric $\mathrm{SO}_0(p,q)$-actions	2010	Gestur Ólafsson Raúl Quiroga-Barranco
+	Representations of compact groups	2008	Jacques Faraut
+	Representations of Lie groups	2024	Pavel Etingof
+ PDF Chat	PseudoRiemannian geometry and actions of simple Lie groups	2005	Raúl Quiroga-Barranco

Works That Cite This (36)

Action	Title	Year	Authors
+	Variants of Kazhdan’s property for subgroups of semisimple groups	1989	Alexander Lubotzky Robert J. Zimmer
+	None	2001	David Fisher Kevin Whyte
+	Unitary spectrum and the fundamental group for actions of semisimple Lie groups	1990	Robert J. Zimmer
+	Superrigidity, ratner’s theorem, and fundamental groups	1991	Robert J. Zimmer
+	Fundamental groups of negatively curved manifolds and actions of semisimple groups	1991	Ralf Spatzier Robert J. Zimmer
+	On the algebraic hull of an automorphism group of a principal bundle	1990	Robert J. Zimmer
+	Ergodic Theory, Groups, and Geometry	2008	Robert J. Zimmer Dave Witte Morris
+	Connection preserving actions are topologically engaging	2012	Alberto Candel Raúl Quiroga-Barranco
+	Kazhdan Groups, Cocycles and Trees	1990	Scot Adams Ralf Spatzier
+	Groups acting on manifolds: around the Zimmer program	2008	David Fisher

Works Cited by This (15)

Action	Title	Year	Authors
+	Ergodic Theory and Semisimple Groups	1984	Robert J. Zimmer
+	Stable Real Cohomology of Arithmetic Groups II	1981	Armand Borel
+	Continuous Cohomology, Discrete Subgroups, and Representations of Reductive Groups	2000	A. Borel Nolan R. Wallach
+	Variants of Kazhdan’s property for subgroups of semisimple groups	1989	Alexander Lubotzky Robert J. Zimmer
+ PDF Chat	Orbit equivalence and rigidity of ergodic actions of Lie groups	1981	Robert J. Zimmer
+ PDF Chat	Arithmeticity of holonomy groups of Lie foliations	1988	Robert J. Zimmer
+	On the Existence of Irreducible Discrete Subgroups in Isotypic Lie Groups of Classical Type	1988	F. E. A. Johnson
+ PDF Chat	Residually finite groups	1969	Wilhelm Magnus
+	Ergodic Therory and the Automorphism Group of a G-Structure	1987	Robert J. Zimmer
+	Kazhdan Groups, Cocycles and Trees	1990	Scot Adams Ralf Spatzier