DC Field | Value | Language |
---|---|---|
dc.contributor.advisor | Suh, Dong-Youp | - |
dc.contributor.advisor | 서동엽 | - |
dc.contributor.author | Park, Dae-Heui | - |
dc.contributor.author | 박대희 | - |
dc.date.accessioned | 2015-04-23T07:54:33Z | - |
dc.date.available | 2015-04-23T07:54:33Z | - |
dc.date.issued | 2001 | - |
dc.identifier.uri | http://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=166359&flag=dissertation | - |
dc.identifier.uri | http://hdl.handle.net/10203/197750 | - |
dc.description | 학위논문(박사) - 한국과학기술원 : 수학전공, 2001.2, [ vii, 106 p. ; ] | - |
dc.description.abstract | The topological properties of semialgebraic actions of semialgebraic groups on semialgebraic sets are studied. Let $G$ be a compact semialgebraic group. We prove that every semialgebraic $G$-set with finitely many orbit types has a semialgebraic $G$-$\CW$ complex structure. Using this result, we also prove that every semialgebraic $G$-set with finitely many orbit types admits a semialgebraic $G$-embedding into some semialgebraic orthogonal representation space of $G$ for $G$ a compact semialgebraic linear group. An affine semialgebraic $G$-set means a semialgebraic $G$-set which is semialgebraically $G$-homeomorphic to a $G$-invariant semialgebraic set in some semialgebraic representation space of $G$. Let $M$ and $N$ be affine semialgebraic $G$-sets. We find a one to one correspondence between the set of semialgebraic $G$-homotopy classes of semialgebraic $G$-maps from $M$ to $N$ and that of topological $G$-homotopy classes of continuous $G$-maps from $M$ to $N$. We also deal with the equivariant semialgebraic version of a theorem of J. H. C. Whitehead. We also deal with semialgebraic $G$-vector bundles. It is proved that any semialgebraic $G$-vector bundle over an affine semialgebraic $G$-set has a semialgebraic classifying $G$-map. Moreover, we prove that the set of semialgebraic $G$-isomorphism classes of semialgebraic $G$-vector bundles over an affine semialgebraic $G$-set $M$ corresponds bijectively to the set of topological $G$-isomorphism classes of topological $G$-vector bundles over $M$. Finally, we construct the equivariant Whitehead group of affine semialgebraic $G$-sets. It is shown that there is a well-defined Whitehead torsion for any $G$-homotopy equivalence between affine semialgebraic $G$-sets. We also prove the semialgebraic invariance of the Whitehead torsion. Moreover, we construct the restricti... | eng |
dc.language | eng | - |
dc.publisher | 한국과학기술원 | - |
dc.subject | transformation group theory | - |
dc.subject | 벡터 번들 | - |
dc.subject | 호모토피 | - |
dc.subject | 준 대수적 집합 | - |
dc.subject | 변환군론 | - |
dc.subject | semialgebraic set | - |
dc.subject | homotopy | - |
dc.subject | vector bundle | - |
dc.title | Topological properties of semialgebraic $G$-Sets | - |
dc.title.alternative | 준 대수적 $G$-집합의 위상적 특성에 관한 연구 | - |
dc.type | Thesis(Ph.D) | - |
dc.identifier.CNRN | 166359/325007 | - |
dc.description.department | 한국과학기술원 : 수학전공, | - |
dc.identifier.uid | 000935138 | - |
dc.contributor.localauthor | Suh, Dong-Youp | - |
dc.contributor.localauthor | 서동엽 | - |
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