Knot adjacency, genus and essential tori
Knot adjacency, genus and essential tori
复制标题
结邻接、属和必要环面
DOI：
10.2140/pjm.2006.228.251
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发表时间：
2004
影响因子：
0.6
通讯作者：
Xiaoxia Lin
中科院分区：
文献类型：
--
作者：
Efstratia Kalfagianni;Xiaoxia Lin
A knot K is called n-adjacent to another knot K' if K admits a projection containing n generalized crossings such that changing any 0 < m = n of them yields a projection of K'. We apply techniques from the theory of sutured 3-manifolds, Dehn surgery and the theory of geometric structures of 3-manifolds to study the extent to which nonisotopic knots can be adjacent to each other. A consequence of our main result is that if K is n-adjacent to K' for all n in N, then K and K' are isotopic. This provides a partial verification of the conjecture of V. Vassiliev that finite type knot invariants distinguish all knots. We also show that if no twist about a crossing circle L of a knot K changes the isotopy class of K, then L bounds a disc in the complement of K. This leads to a characterization of nugatory crossings on knots.
关于强 n-平凡结
DOI：
--
发表时间：
2006
期刊：
影响因子：
--
作者：
Toshiaki;ADACHI;足利 正;足利 正;足利 正;足利 正;足利 正;鳥巣伊知郎
通讯作者：
鳥巣伊知郎