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H(2)-Unknotting Number of a Knot

$H(2)$-Unknotting Number of a Knot

Year:    2009

Author:    Taizo Kanenobu, Yasuyuki Miyazawa

Communications in Mathematical Research , Vol. 25 (2009), Iss. 5 : pp. 433–460

Abstract

An H(2)-move is a local move of a knot which is performed by adding a half-twisted band. It is known an H(2)-move is an unknotting operation. We define the H(2)-unknotting number of a knot K to be the minimum number of H(2)-moves needed to transform K into a trivial knot. We give several methods to estimate the H(2)-unknotting number of a knot. Then we give tables of H(2)-unknotting numbers of knots with up to 9 crossings.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/2009-CMR-19362

Communications in Mathematical Research , Vol. 25 (2009), Iss. 5 : pp. 433–460

Published online:    2009-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    28

Keywords:    knot H(2)-move H(2)-unknotting number signature Arf invariant Jones polynomial Q polynomial.

Author Details

Taizo Kanenobu Email

Yasuyuki Miyazawa Email