Geometriae Dedicata

, Volume 87, Issue 1–3, pp 181–189 | Cite as

Continuous Quotients for Lattice Actions on Compact Spaces

  • David Fisher
  • Kevin Whyte
Article

Abstract

Let Γ < SLn(\(\mathbb{Z}\)) be a subgroup of finite index, where n ≥ 5. Suppose Γ acts continuously on a manifold M, where π1(M) = \(\mathbb{Z}\)n, preserving a measure that is positive on open sets. Further assume that the induced Γ action on H1(M) is non-trivial. We show there exists a finite index subgroup Γ′ < Γ and a Γ′ equivariant continuous map ψ : M\(\mathbb{T}\)n that induces an isomorphism on fundamental group. We prove more general results providing continuous quotients in cases where π1(M) surjects onto a finitely generated torsion free nilpotent group. We also give some new examples of manifolds with Γ actions.

large group actions rigidity ergodic theory and semisimple groups 

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Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • David Fisher
    • 1
  • Kevin Whyte
    • 2
  1. 1.Department of MathematicsYale UniversityNew HavenU.S.A.
  2. 2.Department of MathematicsUniversity of ChicagoChicagoU.S.A.

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