トポロジー火曜セミナー
過去の記録 ~10/09|次回の予定|今後の予定 10/10~
開催情報 | 火曜日 17:00~18:30 数理科学研究科棟(駒場) 056号室 |
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担当者 | 河澄 響矢, 北山 貴裕, 逆井卓也 |
セミナーURL | http://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index.html |
2011年04月26日(火)
16:30-18:00 数理科学研究科棟(駒場) 056号室
Tea: 16:00 - 16:30 コモンルーム, Lie群論・表現論セミナーと合同
吉野 太郎 氏 (東京大学大学院数理科学研究科)
Topological Blow-up (JAPANESE)
Tea: 16:00 - 16:30 コモンルーム, Lie群論・表現論セミナーと合同
吉野 太郎 氏 (東京大学大学院数理科学研究科)
Topological Blow-up (JAPANESE)
[ 講演概要 ]
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 $S$. Roughly 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 $(\\tilde{X}, S)$.
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 $S$. Roughly 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 $(\\tilde{X}, S)$.