Gromov hyperbolicity and a variation of the Gordian complex

2009/12/05 by Kazuhiro Ichihara, Ichihara, Kazuhiro, In Dae Jong +1
Mathematics · #57M25 #FOS: Mathematics #Geometric Topology (math.GT) #math.GT #msc:57M25

paper · pdf · doi:10.48550/arxiv.0912.0990

9 pages, 6 figures

arxiv created 2010/02/22 · arxiv updated 2010/02/26

Abstract

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.

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