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過去の記録 ～04/19｜次回の予定｜今後の予定 04/20～
| 開催情報 | 水曜日 16:30～18:00 数理科学研究科棟(駒場) 122号室 |
|---|---|
| 担当者 | 河東 泰之 |
| セミナーURL | https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm |
2011年02月18日(金)
10:30-12:00 数理科学研究科棟(駒場) 122号室
Pedram Hekmati 氏 (Univ. Adelaide)
Dirac families and 1-cocycles (ENGLISH)
Pedram Hekmati 氏 (Univ. Adelaide)
Dirac families and 1-cocycles (ENGLISH)
[ 講演概要 ]
Families of Dirac type operators, transforming covariantly under the projective action of the loop group $LG$, determine a class in twisted K-theory on compact Lie groups $G$. The loop group is the gauge group of a principal $G$-bundle over the circle and an interesting problem is to try to generalise the circle to a higher dimensional compact manifold. This is far from obvious and some of the difficulties can be modelled in a slightly simpler setting, by replacing $LG$ and gauge connections by objects which have only small differentiability in the Sobolev sense. In this talk, I will provide some background to this problem and explain how 1-cocycles naturally appear in this construction.
Families of Dirac type operators, transforming covariantly under the projective action of the loop group $LG$, determine a class in twisted K-theory on compact Lie groups $G$. The loop group is the gauge group of a principal $G$-bundle over the circle and an interesting problem is to try to generalise the circle to a higher dimensional compact manifold. This is far from obvious and some of the difficulties can be modelled in a slightly simpler setting, by replacing $LG$ and gauge connections by objects which have only small differentiability in the Sobolev sense. In this talk, I will provide some background to this problem and explain how 1-cocycles naturally appear in this construction.
