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Hyperbolicity equations for pseudo hyperbolic structures of knot complements : 매듭 여공간에서 의쌍곡구조를 위한 쌍곡 방정식
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- Authors
- Advisor
- 김홍종, 김혁
- Major
- 자연과학대학 수리과학부
- Issue Date
- 2018-08
- Publisher
- 서울대학교 대학원
- Description
- 학위논문 (석사)-- 서울대학교 대학원 : 자연과학대학 수리과학부, 2018. 8. 김홍종, 김혁.
- 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.
- Language
- English
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