On the Segal conjecture for compact Lie groups.
We study properties of the signature function of the torus knot . 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.
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.