Tokyo Journal of Mathematics

The IH-complex of Spatial Trivalent Graphs

Atsushi ISHII and Kengo KISHIMOTO

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Abstract

We define the IH-complex on the set of spatial trivalent graphs by using the IH-move, which is a local spatial move appeared in a study of knotted handlebodies. The IH-distance between two spatial trivalent graphs is defined by the minimal number of IH-moves needed to transform one into the other. It gives a distance function on the IH-complex. We give a lower bound for the IH-distance, and evaluate it.

Article information

Source
Tokyo J. Math., Volume 33, Number 2 (2010), 523-535.

Dates
First available in Project Euclid: 31 January 2011

Permanent link to this document
https://projecteuclid.org/euclid.tjm/1296483486

Digital Object Identifier
doi:10.3836/tjm/1296483486

Mathematical Reviews number (MathSciNet)
MR2779433

Zentralblatt MATH identifier
1213.57010

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

Citation

ISHII, Atsushi; KISHIMOTO, Kengo. The IH-complex of Spatial Trivalent Graphs. Tokyo J. Math. 33 (2010), no. 2, 523--535. doi:10.3836/tjm/1296483486. https://projecteuclid.org/euclid.tjm/1296483486


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