Gromov hyperbolicity and a variation of the Gordian complex

Proceedings of the Japan Academy, Series A. Mathematical Sciences

article

Kazuhiro Ichihara¹  In Dae Jong² 

[1] Department of Mathematics, College of Humanities and Sciences, Nihon University;Osaka City University Advanced Mathematical Institute

关键词: Alexander-Conway polynomial;    Delta-move;    Gromov hyperbolic space;    Gordian complex.;   

DOI  :  10.3792/pjaa.87.17

学科分类：数学（综合）

来源: Japan Academy

【 摘 要 】

We introduce new simplicial complexes by using various invariants and local moves for knots, which give generalizations of the Gordian complex defined by Hirasawa and Uchida. In particular, we focus on the simplicial complex defined by using the Alexander-Conway polynomial and the Delta-move, and show that the simplicial complex is Gromov hyperbolic and quasi-isometric to the real line.

【 授权许可】

Unknown