Heegaard splittings of knot and link complements = 매듭과 고리의 여공간의 히가드 분리

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We mainly focus on the stabilization problem of Heegaard splittings of knot and link complements in $S^3$. We give a condition for a pair of unknotting tunnels of a non-trivial tunnel number one link to give a genus three Heegaard splittings of the link complement and show that every 2-bridge link has such a pair of unknotting tunnels. For the tunnel number one knot, we give a more restrictive condition for a pair of unknotting tunnels of a non-trivial tunnel number one knot to give a genus three Heegaard splittings of the knot complements and show that every 2-bridge knot has such a pair of unknotting tunnels. In addition, we consider the disjoint curve property for Heegaard splittings of tunnel number one knot complements. We also list the knot types or types of core of the compression body having the d.c.p(disjoint curve property).
Advisors
Jin, Gyo-Taekresearcher진교택researcher
Description
한국과학기술원 : 수학전공,
Publisher
한국과학기술원
Issue Date
2005
Identifier
249400/325007  / 020005245
Language
eng
Description

학위논문(박사) - 한국과학기술원 : 수학전공, 2005.8, [ v, 37 p. ]

Keywords

안정화; 터널; 매듭; 히가드 분리; stabilization; tunnel; knot; Heegaard splitting

URI
http://hdl.handle.net/10203/41884
Link
http://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=249400&flag=dissertation
Appears in Collection
MA-Theses_Ph.D.(박사논문)
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