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

• Autorzy: Tatsuhiko Yagasaki
• Języki publikacji: EN

Abstrakty

EN

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 $ℋ_{E}(M,ω)$.

Kategorie tematyczne

• 58C35: Integration on manifolds; measures on manifolds
• 57S05: Topological properties of groups of homeomorphisms or diffeomorphisms

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2007
• Tom: 197
• Numer: 1
• Strony: 271-287

Daty

wydano

2007

Twórcy

autor

Tatsuhiko Yagasaki

• Division of Mathematics, Faculty of Engineering and Design, Kyoto Institute of Technology, Matsugasaki, Sakyoku, Kyoto 606-8585, Japan

Identyfikatory

DOI

10.4064/fm197-0-13