Proceedings of the Japan Academy, Series A, Mathematical Sciences

Gromov hyperbolicity and a variation of the Gordian complex

Kazuhiro Ichihara and In Dae Jong

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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.

Article information

Proc. Japan Acad. Ser. A Math. Sci. Volume 87, Number 2 (2011), 17-21.

First available in Project Euclid: 1 February 2011

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Zentralblatt MATH identifier

Primary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45}

Alexander-Conway polynomial Delta-move Gromov hyperbolic space Gordian complex


Ichihara, Kazuhiro; Jong, In Dae. Gromov hyperbolicity and a variation of the Gordian complex. Proc. Japan Acad. Ser. A Math. Sci. 87 (2011), no. 2, 17--21. doi:10.3792/pjaa.87.17.

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