Survey on Cappell-Shaneson homotopy 4-sphereCappell-Shaneson 호모토피 4차원 구에 대한 조사

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dc.contributor.advisorPark, JungHwan-
dc.contributor.advisor박정환-
dc.contributor.authorLee, Jaewon-
dc.date.accessioned2023-06-23T19:31:54Z-
dc.date.available2023-06-23T19:31:54Z-
dc.date.issued2022-
dc.identifier.urihttp://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=1008302&flag=dissertationen_US
dc.identifier.urihttp://hdl.handle.net/10203/308917-
dc.description학위논문(석사) - 한국과학기술원 : 수리과학과, 2022.8,[iv, 47 p. :]-
dc.description.abstractCappell and Shaneson constructed a family of homotopy 4-spheres in 1976, and some of them are double covers of an exotic $\mathbb{R}P^4$. They are well-known potential counterexamples for the 4-dimensional smooth Poincaré conjecture. The manifolds are parametrized by a matrix $A\in SL(\mathbb{Z}, 3)$ such that $\det (I-A)=-1$, and $\epsilon\in\mathbb{Z}_2$, which represents a framing of gluing map of $S^2\times D^2$. In this paper, we focus on $\Sigma_m^{\epsilon}$ constructed by smaller family $A_m$ depending only on an integer $m$. In fact, every $A_m^\epsilon$ turns out to be diffeomorphic to the standard sphere $S^4$. This paper is based on papers of Cappell, Shaneson, Akbulut, Kirby, Aitchison, Rubinstein, and Gompf, and follows the proofs in historical order as a survey paper with no author's own result. For the proof of Gompf, in particular, we give more details with handle calculus and isotopy.-
dc.languageeng-
dc.publisher한국과학기술원-
dc.subjectCappell-Shaneson homotopy 4-sphere▼aPoincaré conjecture▼aGluck construction▼aKirby calculus▼aAndrews-Curtis conjecture-
dc.subjectCappell-Shaneson 호모토피 4차원 구▼a푸엥카레 추측▼aGluck 구성▼aKirby 계산▼aAndrews-Curtis 추측-
dc.titleSurvey on Cappell-Shaneson homotopy 4-sphere-
dc.title.alternativeCappell-Shaneson 호모토피 4차원 구에 대한 조사-
dc.typeThesis(Master)-
dc.identifier.CNRN325007-
dc.description.department한국과학기술원 :수리과학과,-
dc.contributor.alternativeauthor이재원-
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