Gromov hyperbolicity and a variation of the Gordian complex

Details Gromov hyperbolicity and a variation of the Gordian complex Gromov hyperbolicity and a variation of the Gordian complex

2009-12-05

arxiv.org/abs/0912.0990v2

Mathematics

Geometric Topology

9 pages, 6 figures

Scientific paper

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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