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Proceedings of the Japan Academy. Series A
Article . 2011 . Peer-reviewed
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Proceedings of the Japan Academy. Series A
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arXiv.org e-Print Archive
Preprint . 2009
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Other literature type . 2011
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https://dx.doi.org/10.48550/ar...
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Gromov hyperbolicity and a variation of the Gordian complex

descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 01 Feb 2011Embargo end date: 01 Jan 2009Publisher:Project EuclidJournal:Proceedings of the Japan Academy, Series A, Mathematical Sciences, volume 87 (issn: 0386-2194, Copyright policy )
Authors: Ichihara, Kazuhiro; Jong, In Dae;

doi: 10.3792/pjaa.87.17 , 10.48550/arxiv.0912.0990

arXiv: http://arxiv.org/abs/0912.0990

Gromov hyperbolicity and a variation of the Gordian complex

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.

9 pages, 6 figures

Related Organizations
Keywords

Alexander-Conway polynomial, Mathematics - Geometric Topology, 57M25, FOS: Mathematics, Geometric Topology (math.GT), Gromov hyperbolic space, Gordian complex, Delta-move

  • BIP!
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    This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    		 4
    popularity
    This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
    		 Average
    influence
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    impulse
    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
4
Average
Average
Average
Green
gold