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

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Yagasaki T.

Fundamenta Mathematicae

2007

tom 197

nr 1

271-287

Suppose M is a noncompact connected n-manifold and ω is a good Radon measure of M with ω(∂M) = 0. Let ℋ(M,ω) denote the group of ω-preserving homeomorphisms of M equipped with the compact-open topology, and $ℋ_{E}(M,ω)$ the subgroup consisting of all h ∈ ℋ(M,ω) which fix the ends of M. S. R. Alpern and V. S. Prasad introduced the topological vector space 𝓢(M,ω) of end charges of M and the end charge homomorphism $c^{ω}: ℋ_{E}(M,ω) → 𝓢(M,ω)$, which measures for each $h ∈ ℋ_{E}(M,ω)$ the mass flow toward ends induced by h. We show that the map $c^{ω}$ has a continuous section. This induces the factorization $ℋ_{E}(M,ω) ≅ Ker c^{ω} × 𝓢(M,ω)$ and implies that $Ker c^{ω}$ is a strong deformation retract of $ℋ_{E}(M,ω)$.

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1 Fundamenta Mathematicae

1 Yagasaki T.

1 2007

Wyniki wyszukiwania

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