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On the Signatures of Torus Knots

Maciej Borodzik, Krzysztof Oleszkiewicz (2010)

Bulletin of the Polish Academy of Sciences. Mathematics

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.

On the simple connectivity at infinity of groups

Daniele Ettore Otera (2003)

Bollettino dell'Unione Matematica Italiana

We study the simple connectivity at infinity of groups of finite presentation, and we give a geometric proof of its invariance under quasi-isometry in a special case.

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