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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.

On the structure of a Morse form foliation

I. Gelbukh (2009)

Czechoslovak Mathematical Journal

The foliation of a Morse form ω on a closed manifold M is considered. Its maximal components (cylinders formed by compact leaves) form the foliation graph; the cycle rank of this graph is calculated. The number of minimal and maximal components is estimated in terms of characteristics of M and ω . Conditions for the presence of minimal components and homologically non-trivial compact leaves are given in terms of rk ω and Sing ω . The set of the ranks of all forms defining a given foliation without minimal...

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