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Scharlemann–Thompson Invariant for Knots with Unknotting Tunnels and the Distance of (1,1)‐Splittings
Author(s) -
Saito Toshio
Publication year - 2005
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610705006514
Subject(s) - knot (papermaking) , invariant (physics) , mathematics , combinatorics , knot theory , finite type invariant , knot invariant , pure mathematics , mathematical physics , mathematical analysis , engineering , invariant polynomial , matrix polynomial , chemical engineering , polynomial
Scharlemann and Thompson introduced an invariant ρ(K,γ)∈ Q/2Z for the pair of a knot K in the 3‐sphere and an unknotting tunnel γ for K . The paper studies the relationship between the invariant ρ(K, γ) of a (1,1)‐knot and the distance of its (1,1)‐splitting introduced by the author.
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