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Lie群論・表現論セミナー
過去の記録 ～04/24｜次回の予定｜今後の予定 04/25～
| 開催情報 | 火曜日 16:30～18:00 数理科学研究科棟(駒場) 126号室 |
|---|---|
| 担当者 | 小林俊行 |
| セミナーURL | https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html |
2008年11月25日(火)
16:30-18:00 数理科学研究科棟(駒場) 126号室
吉野太郎 氏 (東工大)
$\\mathbb R^n$への$\\mathbb R^2$の固有な作用と周期性
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html
吉野太郎 氏 (東工大)
$\\mathbb R^n$への$\\mathbb R^2$の固有な作用と周期性
[ 講演概要 ]
Consider $\\R^2$ actions on $\\R^n$ which is free, affine and unipotent. Our concern here is to answer the following question:
"Does the quotient topology admits a manifold structure?"
Under some weak assumption, we classify all actions up to conjugate, and give a complete answer to the question.
If Lipsman's conjecture were true, all of the answer should be affirmative.
But, we shall find a unique action which gives a negative answer for each $n\\geq 5$. And, we also find a periodicity on such counterexamples.
As a key lemma, we use "proper analogue" of the five lemma on
exact sequence.
[ 参考URL ]Consider $\\R^2$ actions on $\\R^n$ which is free, affine and unipotent. Our concern here is to answer the following question:
"Does the quotient topology admits a manifold structure?"
Under some weak assumption, we classify all actions up to conjugate, and give a complete answer to the question.
If Lipsman's conjecture were true, all of the answer should be affirmative.
But, we shall find a unique action which gives a negative answer for each $n\\geq 5$. And, we also find a periodicity on such counterexamples.
As a key lemma, we use "proper analogue" of the five lemma on
exact sequence.
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html
