Gromov hyperbolicity and a variation of the Gordian complex

Kazuhiro Ichihara; In Dae Jong

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arXiv · 0912.0990

Gromov hyperbolicity and a variation of the Gordian complex

Kazuhiro Ichihara·In Dae Jong

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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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BibTeX RIS

Kazuhiro Ichihara, In Dae Jong. 2010-02-22. Gromov hyperbolicity and a variation of the Gordian complex. https://arxiv.org/abs/0912.0990

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