Continuous quotients for lattice actions on compact manifolds

Details Continuous quotients for lattice actions on compact manifolds Continuous quotients for lattice actions on compact manifolds

2004-05-14

arxiv.org/abs/math/0405273v1

Geometriae Dedicata 87, 2001

Mathematics

Dynamical Systems

Scientific paper

Let G be a subgroup of finite index in SL(n,Z) for N > 4. Suppose G acts continuously on a manifold M, with fundamental group Z^n, preserving a measure that is positive on open sets. Further assume that the induced G action on H^1(M) is non-trivial. We show there exists a finite index subgroup G' of G and a G' equivariant continuous map from M to the n-torus that induces an isomorphism on fundamental groups. We prove more general results providing continuous quotients in cases where the fundamental group of M surjects onto a finitely generated torsion free nilpotent group. We also give some new examples of manifolds with G actions to which the theorems apply.

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