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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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.

Article information

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

Dates
First available in Project Euclid: 1 February 2011

Permanent link to this document
https://projecteuclid.org/euclid.pja/1296570389

Digital Object Identifier
doi:10.3792/pjaa.87.17

Mathematical Reviews number (MathSciNet)
MR2797579

Zentralblatt MATH identifier
1218.57006

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

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

Citation

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. https://projecteuclid.org/euclid.pja/1296570389.


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