Manifolds with infinitely many actions of an arithmetic group
type: Item
instance of: scholarly article
title: Manifolds with infinitely many actions of an arithmetic group
zbMATH Open document ID: 0706.57020
author: Richard K. Lashof
author: Robert J. Zimmer
published in: Illinois Journal of Mathematics
publication date: 1990-01-01T00:00:00Z
review text: Cocompact discrete subgroups \(\Gamma\) of SL(n,\({\mathbb{R}})\) and SU(p,q) together with manifolds M are described such that there are infinitely many \(\Gamma\)-actions on M mutually not conjugate in Diff(M), Homeo(M) and Meas(M). Here Meas(M) is the group of measure class preserving automorphisms. Each such action leaves a smooth metric invariant and every \(\Gamma\) orbit is dense. This is proved - embedding \(\Gamma\)- from: Thm.2: There is a family of non-equivalent tori \(T_ k<SU(n)\times SU(n)\) with \(SU(n)\times SU(n)/T_ k\) all diffeomorphic. Choosing the \(T_ k\) as graphs over a torus T in the first SU(n)-factor, conjugacy can be checked easily. The assertion then follows from a sufficiently fine classification of the SU(n)-bundles \(SU(n)\times SU(n)/T_ k\to SU(n)/T\).
Mathematics Subject Classification ID: 57S20
Mathematics Subject Classification ID: 22E40
zbMATH DE Number: 4159652
zbMATH Keywords: diffeomorphism group
zbMATH Keywords: homeomorphism group
zbMATH Keywords: actions of arithmetic groups
zbMATH Keywords: cocompact discrete subgroups of SL(n,\({\mathbb{R}})\) and SU(p,q)
zbMATH Keywords: measure class preserving automorphisms
MaRDI profile type: Publication
Recommended article: Arithmetic groups acting on compact manifolds
Recommended article: Actions of arithmetic groups on homology spheres and acyclic homology manifolds
Recommended article: Actions of finite groups on compact manifolds
Recommended article: Infinite-dimensional manifold triples of homeomorphism groups
Recommended article: Large group actions on manifolds
Recommended article: Manifolds with non-stable fundamental groups at infinity
Recommended article: Actions of certain arithmetic groups on Gromov hyperbolic spaces
Recommended article: Q3312962
Recommended article: Manifolds with group actions and elliptic operators
Recommended article: Almost fixed points of finite group actions on manifolds without odd cohomology
description: scientific article; zbMATH DE number 4159652