Journal of the Mathematical Society of Japan

The Gordian distance of handlebody-knots and Alexander biquandle colorings

Tomo MURAO

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Abstract

We give lower bounds for the Gordian distance and the unknotting number of handlebody-knots by using Alexander biquandle colorings. We construct handlebody-knots with Gordian distance $n$ and unknotting number $n$ for any positive integer $n$.

Article information

Source
J. Math. Soc. Japan, Volume 70, Number 4 (2018), 1247-1267.

Dates
Received: 28 February 2017
First available in Project Euclid: 27 July 2018

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1532678872

Digital Object Identifier
doi:10.2969/jmsj/77417741

Mathematical Reviews number (MathSciNet)
MR3868206

Zentralblatt MATH identifier
07009701

Subjects
Primary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45}
Secondary: 57M15: Relations with graph theory [See also 05Cxx] 57M27: Invariants of knots and 3-manifolds

Keywords
handlebody-knot biquandle Gordian distance unknotting number

Citation

MURAO, Tomo. The Gordian distance of handlebody-knots and Alexander biquandle colorings. J. Math. Soc. Japan 70 (2018), no. 4, 1247--1267. doi:10.2969/jmsj/77417741. https://projecteuclid.org/euclid.jmsj/1532678872


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