Geodesic
On the Signatures of Torus Knots
Maciej Borodzik1 ; Krzysztof Oleszkiewicz2
1Institute of Mathematics University of Warsaw Banacha 2 02-097 Warsaw, Poland
2Institute 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
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 58 (2010) no. 2, pp. 167-177
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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.
DOI : 10.4064/ba58-2-7
Keywords: study properties signature function torus knot first provide elementary proof formula integral signature circle obtain closed formula tristram levine signature torus knot terms dedekind sums

Maciej Borodzik  1   ; Krzysztof Oleszkiewicz  2

1 Institute of Mathematics University of Warsaw Banacha 2 02-097 Warsaw, Poland
2 Institute 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 
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Maciej Borodzik; Krzysztof Oleszkiewicz. On the Signatures of Torus Knots. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 58 (2010) no. 2, pp. 167-177. doi: 10.4064/ba58-2-7

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