Tuesday Seminar on Topology

Seminar information archive ~03/28Next seminarFuture seminars 03/29~

Date, time & place Tuesday 17:00 - 18:30 056Room #056 (Graduate School of Math. Sci. Bldg.)
Organizer(s) KAWAZUMI Nariya, KITAYAMA Takahiro, SAKASAI Takuya

2009/01/13

16:30-17:30   Room #002 (Graduate School of Math. Sci. Bldg.)
山下 温 (東京大学大学院数理科学研究科)
Compactification of the homeomorphism group of a graph
[ Abstract ]
Topological properties of homeomorphism groups, especially of finite-dimensional manifolds,
have been of interest in the area of infinite-dimensional manifold topology.
For a locally finite graph $\\Gamma$ with countably many components,
the homeomorphism group $\\mathcal{H}(\\Gamma)$
and its identity component $\\mathcal{H}_+(\\Gamma)$ are topological groups
with respect to the compact-open topology. I will define natural compactifications
$\\overline{\\mathcal{H}}(\\Gamma)$ and
$\\overline{\\mathcal{H}}_+(\\Gamma)$ of these groups and describe the
topological type of the pair $(\\overline{\\mathcal{H}}_+(\\Gamma), \\mathcal{H}_+(\\Gamma))$
using the data of $\\Gamma$. I will also discuss the topological structure of
$\\overline{\\mathcal{H}}(\\Gamma)$ where $\\Gamma$ is the circle.