Lie Groups and Representation Theory

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

2008/11/25

16:30-18:00   Room #126 (Graduate School of Math. Sci. Bldg.)
吉野太郎 (東工大)
$\\mathbb R^n$への$\\mathbb R^2$の固有な作用と周期性
[ Abstract ]
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.
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html