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

Tatsuhiko Yagasaki. "Measure-preserving homeomorphisms of noncompact manifolds and mass flow toward ends." Fundamenta Mathematicae 197.1 (2007): 271-287. <http://eudml.org/doc/286576>.

@article{TatsuhikoYagasaki2007,
abstract = {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 (M,ω) of end charges of M and the end charge homomorphism $c^\{ω\}: ℋ_\{E\}(M,ω) → (M,ω)$, 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 $ℋ_\{E\}(M,ω) ≅ Ker c^\{ω\} × (M,ω)$ and implies that $Ker c^\{ω\}$ is a strong deformation retract of $ℋ_\{E\}(M,ω)$.},
author = {Tatsuhiko Yagasaki},
journal = {Fundamenta Mathematicae},
keywords = {group of measure-preserving homeomorphisms; mass flow; end charge; noncompact manifold},
language = {eng},
number = {1},
pages = {271-287},
title = {Measure-preserving homeomorphisms of noncompact manifolds and mass flow toward ends},
url = {http://eudml.org/doc/286576},
volume = {197},
year = {2007},
}

TY - JOUR
AU - Tatsuhiko Yagasaki
TI - Measure-preserving homeomorphisms of noncompact manifolds and mass flow toward ends
JO - Fundamenta Mathematicae
PY - 2007
VL - 197
IS - 1
SP - 271
EP - 287
AB - 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 (M,ω) of end charges of M and the end charge homomorphism $c^{ω}: ℋ_{E}(M,ω) → (M,ω)$, 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 $ℋ_{E}(M,ω) ≅ Ker c^{ω} × (M,ω)$ and implies that $Ker c^{ω}$ is a strong deformation retract of $ℋ_{E}(M,ω)$.
LA - eng
KW - group of measure-preserving homeomorphisms; mass flow; end charge; noncompact manifold
UR - http://eudml.org/doc/286576
ER -