DC Field | Value | Language |
---|---|---|
dc.contributor.advisor | Park, JungHwan | - |
dc.contributor.advisor | 박정환 | - |
dc.contributor.author | Lee, Jaewon | - |
dc.date.accessioned | 2023-06-23T19:31:54Z | - |
dc.date.available | 2023-06-23T19:31:54Z | - |
dc.date.issued | 2022 | - |
dc.identifier.uri | http://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=1008302&flag=dissertation | en_US |
dc.identifier.uri | http://hdl.handle.net/10203/308917 | - |
dc.description | 학위논문(석사) - 한국과학기술원 : 수리과학과, 2022.8,[iv, 47 p. :] | - |
dc.description.abstract | Cappell 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.language | eng | - |
dc.publisher | 한국과학기술원 | - |
dc.subject | Cappell-Shaneson homotopy 4-sphere▼aPoincaré conjecture▼aGluck construction▼aKirby calculus▼aAndrews-Curtis conjecture | - |
dc.subject | Cappell-Shaneson 호모토피 4차원 구▼a푸엥카레 추측▼aGluck 구성▼aKirby 계산▼aAndrews-Curtis 추측 | - |
dc.title | Survey on Cappell-Shaneson homotopy 4-sphere | - |
dc.title.alternative | Cappell-Shaneson 호모토피 4차원 구에 대한 조사 | - |
dc.type | Thesis(Master) | - |
dc.identifier.CNRN | 325007 | - |
dc.description.department | 한국과학기술원 :수리과학과, | - |
dc.contributor.alternativeauthor | 이재원 | - |
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