Monday, March 10th, 2003
11:30am - 12:30pm, in Science 1- Small Auditorium

Daniel Matei

University of Tokyo

Counting Solvable Representations of Knot Groups

Abstract: For G a knot group and S a finite solvable group we describe a recursive procedure for computing the number of epimorphisms of onto S in terms of the Alexander ideals of the knot and the factors of a composition series of S. The key ingredients to our approach are the degree 1 and 2 cohomology groups of G with coefficients in a local system and the Mobius function of the lattice of subgroups of S. As an application, we give formulae for the number of index n subgroups of G, for low values of n.