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February 2011 Gromov hyperbolicity and a variation of the Gordian complex
Kazuhiro Ichihara, In Dae Jong
Proc. Japan Acad. Ser. A Math. Sci. 87(2): 17-21 (February 2011). DOI: 10.3792/pjaa.87.17

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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Kazuhiro Ichihara. In Dae Jong. "Gromov hyperbolicity and a variation of the Gordian complex." Proc. Japan Acad. Ser. A Math. Sci. 87 (2) 17 - 21, February 2011. https://doi.org/10.3792/pjaa.87.17

Information

Published: February 2011
First available in Project Euclid: 1 February 2011

zbMATH: 1218.57006
MathSciNet: MR2797579
Digital Object Identifier: 10.3792/pjaa.87.17

Subjects:
Primary: 57M25

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

Rights: Copyright © 2011 The Japan Academy

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Vol.87 • No. 2 • February 2011
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