On the signatures of torus knots

Maciej Borodzik; Krzysztof Oleszkiewicz

On the signatures of torus knots

Geometric Topology 2010-02-25 v1

Authors: Maciej Borodzik , Krzysztof Oleszkiewicz

Abstract

We study properties of the signature function of the torus knot $T_{p,q}$ . First we provide a very elementary proof of the formula for the integral of the signatures over the circle. We obtain also a closed formula for the Tristram--Levine signature of a torus knot in terms of Dedekind sums.

Keywords

torus knots signature function Tristram-Levine signature Dedekind sums integral formula

Cite

@article{arxiv.1002.4500,
  title  = {On the signatures of torus knots},
  author = {Maciej Borodzik and Krzysztof Oleszkiewicz},
  journal= {arXiv preprint arXiv:1002.4500},
  year   = {2010}
}

Comments

10 pages

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