Publications
Detailed Information
Hyperbolicity equations for pseudo hyperbolic structures of knot complements : 매듭 여공간에서 의쌍곡구조를 위한 쌍곡 방정식
| DC Field | Value | Language |
|---|---|---|
| dc.contributor.advisor | 김홍종, 김혁 | - |
| dc.contributor.author | 김우정 | - |
| dc.date.accessioned | 2018-12-03T01:44:31Z | - |
| dc.date.available | 2018-12-03T01:44:31Z | - |
| dc.date.issued | 2018-08 | - |
| dc.identifier.other | 000000153069 | - |
| dc.identifier.uri | https://hdl.handle.net/10371/143897 | - |
| dc.description | 학위논문 (석사)-- 서울대학교 대학원 : 자연과학대학 수리과학부, 2018. 8. 김홍종, 김혁. | - |
| dc.description.abstract | Abstract
A knot complement can be decomposed by the Ideal octahedron mod- ulo two points. In this decomposition, pseudo-developing map and its holonomy representation show the conditions to construct pseudo- hyperbolic structure. The conditions are written as hyperbolicity equa- tion. Therefore, when the shape of each octahedron satisfy the hyper- bolicity equation, we can give a pseudo-hyperbolic structure to the knot complement. In this paper, we consider various kinds of variables to rep- resent and to solve the hyperbolicity equation and especially decide a general algorithm of obtaining w-variable solutions for this equation. Keywords: Knot, octahedral decomposition, pseudo-hyperbolic structure, pseudo-developing. | - |
| dc.description.tableofcontents | 1 Introduction 4
2 Preliminary 5 3 Pseudo-developing and holonomy 6 3.1 Pseudo-developing . . . . . . . . . . . . . . . . . . . . . 7 3.2 The cross-ratio and Thurston's gluing equation . . . . . 9 4 The octahedral decomposition of a knot complement 10 5 Hyperbolicity equation 13 5.1 The cross-ratio in octahedron . . . . . . . . . . . . . . . 13 5.2 α, γ in octahedrons of oriented knot . . . . . . . . . . . 15 5.3 Conditions for satisfying hyperbolicity equation . . . . . 16 5.3.1 Cusp condition for gluing condition and z-variable 17 5.3.2 Region condition for gluing condition and w- variable . . . . . . . . . . . . . . . . . . . . . . . 19 5.4 Relations between | - |
| dc.description.tableofcontents | α, γ, z-variable, τ and w-variable . . . 20
5.5 Corner variable . . . . . . . . . . . . . . . . . . . . . . . 25 6 Solutions of hyperbolicity equation 27 6.1 The Trefoil knot . . . . . . . . . . . . . . . . . . . . . . 27 6.2 The gure eight knot . . . . . . . . . . . . . . . . . . . 29 7 w-variable solution 30 7.1 s-variable and local properties of s-variables . . . . . . . 30 7.2 Algorithm to determine w-variable in some examples . . 33 7.3 Applying the algorithm for w-solutions in some examples 38 8 Bibliography 47 | - |
| dc.format | application/pdf | - |
| dc.format.medium | application/pdf | - |
| dc.language.iso | en | - |
| dc.publisher | 서울대학교 대학원 | - |
| dc.subject.ddc | 510 | - |
| dc.title | Hyperbolicity equations for pseudo hyperbolic structures of knot complements | - |
| dc.title.alternative | 매듭 여공간에서 의쌍곡구조를 위한 쌍곡 방정식 | - |
| dc.type | Thesis | - |
| dc.description.degree | Master | - |
| dc.contributor.affiliation | 자연과학대학 수리과학부 | - |
| dc.date.awarded | 2018-08 | - |
- Appears in Collections:
- Files in This Item:
Item View & Download Count
Items in S-Space are protected by copyright, with all rights reserved, unless otherwise indicated.