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Journal of the London Mathematical Society (1)

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

Journal of the London Mathematical Society / Volume 71 / Issue 3 / June 2005

Published online by Cambridge University Press:

24 May 2005, pp. 801-816

Print publication:

June 2005
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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.