Geodesic
On the Signatures of Torus Knots
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
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 58 (2010) no. 2, pp. 167-177 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

Voir la notice de l'article

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 
@article{10_4064_ba58_2_7,
     author = {Maciej Borodzik and Krzysztof Oleszkiewicz},
     title = {On the {Signatures} of {Torus} {Knots}},
     journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
     pages = {167--177},
     year = {2010},
     volume = {58},
     number = {2},
     doi = {10.4064/ba58-2-7},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/ba58-2-7/}
}
TY  - JOUR
AU  - Maciej Borodzik
AU  - Krzysztof Oleszkiewicz
TI  - On the Signatures of Torus Knots
JO  - Bulletin of the Polish Academy of Sciences. Mathematics
PY  - 2010
SP  - 167
EP  - 177
VL  - 58
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4064/ba58-2-7/
DO  - 10.4064/ba58-2-7
LA  - en
ID  - 10_4064_ba58_2_7
ER  - 
%0 Journal Article
%A Maciej Borodzik
%A Krzysztof Oleszkiewicz
%T On the Signatures of Torus Knots
%J Bulletin of the Polish Academy of Sciences. Mathematics
%D 2010
%P 167-177
%V 58
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4064/ba58-2-7/
%R 10.4064/ba58-2-7
%G en
%F 10_4064_ba58_2_7
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

Cité par Sources :