On the Signatures of Torus Knots

Volume 58 / 2010

Maciej Borodzik, Krzysztof Oleszkiewicz Bulletin Polish Acad. Sci. Math. 58 (2010), 167-177 MSC: Primary 57M25. DOI: 10.4064/ba58-2-7

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 signature over the circle. We also obtain a closed formula for the Tristram–Levine signature of a torus knot in terms of Dedekind sums.

Authors

  • Maciej BorodzikInstitute of Mathematics
    University of Warsaw
    Banacha 2
    02-097 Warsaw, Poland
    e-mail
  • Krzysztof OleszkiewiczInstitute of Mathematics
    University of Warsaw
    Banacha 2
    02-097 Warsaw, Poland
    and
    Institute of Mathematics
    Polish Academy of Sciences
    Śniadeckich 8
    00-956 Warsaw, Poland
    e-mail

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