Actions of homeomorphism groups of manifolds admitting a nontrivial finite free action

2019/09/27 by Chen, Lei
#Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1909.12515

Abstract

In this paper, we study the action of Homeo₀(M), the identity component of the group of homeomorphisms of an n-dimensional manifold M with an \mathbbF_p-free action, on another manifold N of dimension n+k<2n. We prove that if M is not an \mathbbF_p-homology sphere, then N≅ M× K for a homology manifold K such that the action of Homeo₀(M) on M is standard and on K is trivial. In particular, for M=Sⁿ a sphere, any nontrivial action is a generalization of the "coning-off" construction.

Related

• Structure theorems for actions of homeomorphism groups
• Actions of groups of homeomorphisms on one-manifolds
• Groups of homeomorphisms of one-manifolds, I: actions of nonlinear groups
• There are no exotic actions of diffeomorphism groups on 1-manifolds
• Actions of groups of diffeomorphisms on one-manifolds