Gromov hyperbolicity and a variation of the Gordian complex

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 sh...

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Bibliographic Details
Published in:Proceedings of the Japan Academy. Series A. Mathematical sciences 2011-02, Vol.87 (2), p.17-21
Main Authors: Ichihara, Kazuhiro, Jong, In Dae
Format: Article
Language:English
Subjects:
57M25
Alexander-Conway polynomial
Delta-move
Gordian complex
Gromov hyperbolic space
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Summary: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.
ISSN:0386-2194
DOI:10.3792/pjaa.87.17