Mutation invariance of the Arc index for some montesinos knots = 몬테시노스 매듭들에 대한 호지수의 돌연변이 불변성

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Every tame knot or link can be embeded into a finite union of half-planes which have the z-axis as their common boundary, so that each half plane intersects the knot or link in a simple arc. Such an embedding is called an arc presentation and the minimal number of half-planes among all arc presentations is called the arc index of the knot or link. Moreover, we introduce an application of the arc index to the mosaic knots. Mutation is an operation on a knot diagram which replaces a two string tangle with its image under a $180 ^\circ C$ rotation. Mutation may change the knot types. For the alternating knots or links, mutations do not change the arc index. For nonalternating knots and links, some of the semi-alternating knots or links have the same property. We mainly focus on the problem of mutation invariance of the arc index for non alternating knots which are not semi-alternating. We found families of infinitely many mutant pairs/triples of Montesinos knots with the same arc index.
Advisors
Jin, Gyo Taekresearcher진교택researcher
Description
한국과학기술원 :수리과학과,
Publisher
한국과학기술원
Issue Date
2017
Identifier
325007
Language
eng
Description

학위논문(박사) - 한국과학기술원 : 수리과학과, 2017.2,[iv, 38 p :]

Keywords

arc index; mutation; invariance; non semi-alternating; Montesinos knot; 호지수; 돌연변이 변환; 불변성; 비 준교대 매듭; 몬테시노스 매듭

URI
http://hdl.handle.net/10203/241905
Link
http://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=675756&flag=dissertation
Appears in Collection
MA-Theses_Ph.D.(박사논문)
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