The Gordian distance of handlebody-knots and Alexander biquandle colorings

Tomo Murao

doi:10.2969/jmsj/77417741

Journal of the Mathematical Society of Japan

Online ISSN : 1881-1167
Print ISSN : 0025-5645
ISSN-L : 0025-5645

The Gordian distance of handlebody-knots and Alexander biquandle colorings

Tomo Murao

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Keywords: handlebody-knot, biquandle, Gordian distance, unknotting number

JOURNAL FREE ACCESS

2018 Volume 70 Issue 4 Pages 1247-1267

DOI https://doi.org/10.2969/jmsj/77417741

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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.

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