Studies on compact and noncompact semialgebraic transformation groups = 컴팩트와 비컴팩트 준대수적 변환군론에 대한 연구

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Various properties of semialgebraic actions including noncompact case are studied. Let $G$ be a semialgebraic group and $M$ a proper semialgebraic $G$-set. We prove that every point of $M$ has a semialgebraic slice and $M$ can be covered by a finite number of $G$-tubes. Using this, we obtain some pleasant results. We prove that $M$ can be embedded in a $G$-representation space if $G$ is a semialgebraic linear group. Semialgebraic version of the covering homotopy theorem is proved when $G$ is compact. With this, a conjecture introduced by Bredon is completely solved in that semialgebraic category which covers almost all reasonable topological cases. We also show that every proper semialgebraic $G$-set has a semialgebraic $G$-cell decomposition. And finally we introduce the theory of semialgebraic $G$-vector bundles and we show that every semialgebraic $G$-vector bundles over a semialgebraic set is one to one correspondence with topological $G$-vector bundles.
Advisors
Suh, Dong-Youpresearcher서동엽researcher
Description
한국과학기술원 : 수학전공,
Publisher
한국과학기술원
Issue Date
2003
Identifier
231029/325007  / 000985376
Language
eng
Description

학위논문(박사) - 한국과학기술원 : 수학전공, 2003.8, [ iv, 71 p. ]

Keywords

준대수적; 변환군; noncompact; semialgebraic; transformation; 비컴팩트

URI
http://hdl.handle.net/10203/41865
Link
http://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=231029&flag=dissertation
Appears in Collection
MA-Theses_Ph.D.(박사논문)
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