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THE UNKNOTTING NUMBER AND CLASSICAL INVARIANTS II

Published online by Cambridge University Press:  22 August 2014

MACIEJ BORODZIK  and
STEFAN FRIEDL
MACIEJ BORODZIK
Affiliation:
Institute of Mathematics, University of Warsaw, Warsaw, Poland e-mail: mcboro@mimuw.edu.pl
STEFAN FRIEDL
Affiliation:
Mathematisches Institut, Universität zu Köln, Köln, Germany e-mail: sfriedl@gmail.com
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Abstract

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In [3] the authors (M. Borodzik and S. Friedl, Unknotting number and classical invariants (preprint 2012)) associated to a knot K ⊂ S3 an invariant nℝ(K), which is defined using the Blanchfield form and which gives a lower bound on the unknotting number. In this paper, we express nℝ(K) in terms of the Levine-Tristram signatures and nullities of K. We also show in the proof that the Blanchfield form for any knot K is diagonalisable over ℝ[t±1].

Keywords

Primary 57M27
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 56 , Issue 3 , September 2014 , pp. 657 - 680
Copyright
Copyright © Glasgow Mathematical Journal Trust 2014 

References

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