Measure-preserving homeomorphisms of noncompact manifolds and mass flow toward ends

Details Measure-preserving homeomorphisms of noncompact manifolds and mass flow toward ends Measure-preserving homeomorphisms of noncompact manifolds and mass flow toward ends

2005-12-12

arxiv.org/abs/math/0512231v2

Fund. Math., 197 (2007) 271 - 287

Mathematics

Geometric Topology

the published version

Scientific paper

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).

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