Lie Groups and Representation Theory

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

Date, time & place Tuesday 16:30 - 18:00 126Room #126 (Graduate School of Math. Sci. Bldg.)

2011/04/26

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Taro YOSHINO (the University of Tokyo)
Topological Blow-up (JAPANESE)
[ Abstract ]
Suppose that a Lie group $G$ acts on a manifold
$M$. The quotient space $X:=G\\backslash M$ is locally compact,
but not Hausdorff in general. Our aim is to understand
such a non-Hausdorff space $X$.
The space $X$ has the crack $S$. Rougly speaking, $S$ is
the causal subset of non-Hausdorffness of $X$, and especially
$X\\setminus S$ is Hausdorff.

We introduce the concept of `topological blow-up' as a `repair'
of the crack. The `repaired' space $\\tilde{X}$ is
locally compact and Hausdorff space containing $X\\setminus S$
as its open subset. Moreover, the original space $X$ can be
recovered from the pair of $(\\tilde{X}, S)$.