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SCHARLEMANN–THOMPSON INVARIANT FOR KNOTS WITH UNKNOTTING TUNNELS AND THE DISTANCE OF (1,1)-SPLITTINGS

Published online by Cambridge University Press:  24 May 2005

TOSHIO SAITO
TOSHIO SAITO
Affiliation:
Department of Mathematics, Graduate School of Science, Osaka University, Machikaneyama 1-16, Toyonaka, Osaka 560-0043, Japansaito@gaia.math.wani.osaka-u.ac.jp
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Abstract

Scharlemann and Thompson introduced an invariant $\rho(K,\gamma)\in \mathbb{Q}/2\mathbb{Z}$ for the pair of a knot $K$ in the 3-sphere and an unknotting tunnel $\gamma$ for $K$. The paper studies the relationship between the invariant $\rho(K,\gamma)$ of a (1,1)-knot and the distance of its (1,1)-splitting introduced by the author.

Keywords

57M25 (primary)57M27 (secondary)
Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 71 , Issue 3 , June 2005 , pp. 801 - 816
Copyright
The London Mathematical Society 2005

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