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

Fundamenta Mathematicae

2008-04-23T03:01:15Z

2008-04-23T03:01:15Z

2007-12

Suppose M is a noncompact connected n-manifold and m is a good Radon measure of M with m(d 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. S.R.Alpern and V.S.Prasad introduced the topological vector space S(M, m) of end charges of M and the end charge homomorphism c^m : H_E(M; m) to S(M, m), which measures for each h in H_E(M; m)$ the mass flow toward ends induced by h. We show that the map c^m has a continuous section. This induces the factorization H_E(M; m) cong Ker c^m times S(M, m) and implies that Ker c^m is a strong deformation retract of H_E(M; m).

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Published in Fundamenta Mathematicae, Vol 197 (2007) pp. 271-287 (Institute of Mathematics, Polish Academy of Sciences)

http://hdl.handle.net/10212/1660

en

https://doi.org/10.4064/fm197-0-13

Journal Article

Article