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Tight contact structures on hyperbolic 3-manifolds : 3차원 쌍곡 다양체 위의 타이트한 접촉 구조들

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dc.contributor.advisorOtto Van Koert-
dc.contributor.author이주현-
dc.date.accessioned2017-07-14T00:40:01Z-
dc.date.available2017-07-14T00:40:01Z-
dc.date.issued2013-02-
dc.identifier.other000000009269-
dc.identifier.urihttps://hdl.handle.net/10371/121261-
dc.description학위논문 (박사)-- 서울대학교 대학원 : 수리과학부, 2013. 2. Otto Van Koert.-
dc.description.abstract우리는 $\Sigma\times I$의 경계 $\Sigma\times \{0\}$에 임의의 separating 곡선 한 개를 dividing 곡선으로 고정하고, 이 곡선과 두 개의 점에서 만나는 nonseparating 곡선을 택한 다음, $\Sigma\times \{0\}$의 dividing 곡선을 이 곡선의 주위로 임의의 정수 $n$ 번 Dehn 뒤틀림하여 얻은 곡선을 $\Sigma\times \{1\}$의 dividing 곡선으로 생각한다. 이러한 경계 조건 하에서, 우리는 경계의 타이트한 접촉 구조를 내부로 확장한 타이트한 접촉구조 개수의 최소값과 최대값을 조사한다.-
dc.description.tableofcontents1 Introduction : Honda's conjecture 1
2 3-dimensional topology and geometry 5
2.1 Topology of 3-manifolds . . . . . . . . . . . . . . . . . . . . . 5
2.2 Thurston's hyperbolization theorem . . . . . . . . . . . . . . . 9
3 Contact 3-manifolds 24
3.1 Prelimenaries . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.2 Existence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.3 Global structures of overtwisted(OT) contact 3-manifold . . . 29
3.4 Convex surface . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.5 Bypass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.6 Gluing of tight contact manifolds . . . . . . . . . . . . . . . . 43
3.7 Global structures of tight contact 3-manifold . . . . . . . . . . 45
4 Tight contact structures on hyperbolic 3-manifolds 48
4.1 Tight contact structures on hyperbolic surface bundles over
the interval . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
4.2 Proof of Proposition 4.1.5 . . . . . . . . . . . . . . . . . . . . 55
4.3 Proof of Proposition 4.1.4 . . . . . . . . . . . . . . . . . . . . 67
4.4 Proof of Proposition 4.1.6 . . . . . . . . . . . . . . . . . . . . 82
4.5 Proof of Proposition 4.1.3 . . . . . . . . . . . . . . . . . . . . 91
4.6 Proof of Proposition 4.1.7 . . . . . . . . . . . . . . . . . . . . 110
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dc.formatapplication/pdf-
dc.format.extent3792405 bytes-
dc.format.mediumapplication/pdf-
dc.language.isoen-
dc.publisher서울대학교 대학원-
dc.subjectcontact geometry-
dc.subjecttight contact structure-
dc.subjecthyperbolic 3-manifold-
dc.subject.ddc510-
dc.titleTight contact structures on hyperbolic 3-manifolds-
dc.title.alternative3차원 쌍곡 다양체 위의 타이트한 접촉 구조들-
dc.typeThesis-
dc.contributor.AlternativeAuthorJUHYUN LEE-
dc.description.degreeDoctor-
dc.citation.pagesiii,130-
dc.contributor.affiliation자연과학대학 수리과학부-
dc.date.awarded2013-02-
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