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トポロジー火曜セミナー
過去の記録 ～06/13｜次回の予定｜今後の予定 06/14～
| 開催情報 | 火曜日 17:00～18:30 数理科学研究科棟(駒場) 056号室 |
|---|---|
| 担当者 | 河澄 響矢, 北山 貴裕, 逆井卓也, 葉廣和夫 |
| セミナーURL | https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index.html |
2007年01月23日(火)
16:30-18:30 数理科学研究科棟(駒場) 056号室
Tea: 16:00 - 16:30 コモンルーム
中田 文憲 氏 (東京大学大学院数理科学研究科) 16:30-17:30
The twistor correspondence for self-dual Zollfrei metrics
----their singularities and reduction
On the homology group of $Out(F_n)$
Tea: 16:00 - 16:30 コモンルーム
中田 文憲 氏 (東京大学大学院数理科学研究科) 16:30-17:30
The twistor correspondence for self-dual Zollfrei metrics
----their singularities and reduction
[ 講演概要 ]
C. LeBrun and L. J. Mason investigated a twistor-type correspondence
between indefinite conformal structures of signature (2,2) with some properties
and totally real embeddings from RP^3 to CP^3.
In this talk, two themes following LeBrun and Mason are explained.
First we consider an additional structure:
the conformal structure is equipped with a null surface foliation
which has some singularity.
We establish a global twistor correspondence for such structures,
and we show that a low dimensional correspondence
between some quotient spaces is induced from this twistor correspondence.
Next we formulate a certain singularity for the conformal structures.
We generalize the formulation of LeBrun and Mason's theorem
admitting the singularity, and we show explicit examples.
大橋 了 氏 (東京大学大学院数理科学研究科) 17:30-18:30C. LeBrun and L. J. Mason investigated a twistor-type correspondence
between indefinite conformal structures of signature (2,2) with some properties
and totally real embeddings from RP^3 to CP^3.
In this talk, two themes following LeBrun and Mason are explained.
First we consider an additional structure:
the conformal structure is equipped with a null surface foliation
which has some singularity.
We establish a global twistor correspondence for such structures,
and we show that a low dimensional correspondence
between some quotient spaces is induced from this twistor correspondence.
Next we formulate a certain singularity for the conformal structures.
We generalize the formulation of LeBrun and Mason's theorem
admitting the singularity, and we show explicit examples.
On the homology group of $Out(F_n)$
[ 講演概要 ]
Suppose $F_n$ is the free group of rank $n$,
$Out(F_n) = Aut(F_n)/Inn(F_n)$ the outer automorphism group of $F_n$.
We compute $H_*(Out(F_n);\\mathbb{Q})$ for $n\\leq 6$ and conclude
that non-trivial classes in this range are generated
by Morita classes $\\mu_i \\in H_{4i}(Out(F_{2i+2});\\mathbb{Q})$.
Also we compute odd primary part of $H^*(Out(F_4);\\mathbb{Z})$.
Suppose $F_n$ is the free group of rank $n$,
$Out(F_n) = Aut(F_n)/Inn(F_n)$ the outer automorphism group of $F_n$.
We compute $H_*(Out(F_n);\\mathbb{Q})$ for $n\\leq 6$ and conclude
that non-trivial classes in this range are generated
by Morita classes $\\mu_i \\in H_{4i}(Out(F_{2i+2});\\mathbb{Q})$.
Also we compute odd primary part of $H^*(Out(F_4);\\mathbb{Z})$.
