Measure-preserving homeomorphisms of noncompact manifolds and mass flow toward ends
Geometric Topology
2008-02-12 v2 Dynamical Systems
General Topology
Abstract
Suppose M is a noncompact connected n-manifold and m is a good Radon measure of M with m(bdry M) = 0. Let H(M; m) denote the group of m-preserving homeomorphisms of M equipped with the compact-open topology and H_E(M; m) denote the subgroup consisting of all h in H(M; m) which fix the ends of M. Each h in H_E(M; m) moves mass toward ends and this quantity is measured by a mass flow homomorphism J : H_E(M; m) -> V_m, where V_m is a topological vector space. We show that the map J has a continuous section. This induces the factorization H_E(M; m) cong Ker J times V_m and implies that Ker J is a strong deformation retract of H_E(M; m).
Keywords
Cite
@article{arxiv.math/0512231,
title = {Measure-preserving homeomorphisms of noncompact manifolds and mass flow toward ends},
author = {Tatsuhiko Yagasaki},
journal= {arXiv preprint arXiv:math/0512231},
year = {2008}
}
Comments
the published version