Speaker: Thiago de Melo (Rio Claro, Brazylia)

Title of the talk: Torsion and simple homotopy type of quaternionic spherical space forms

Abstract: We obtain a cellular decomposition of the quaternionic spherical space forms, manifolds of positive constant curvature that are factors of an odd sphere by a free action of a generalized quaternionic group. The cellular structure permits to describe the associate chain complex of modules over the integral group ring of the fundamental group, and therefore to compute the Whitehead torsion for any representation of the fundamental group. This provides simple homotopy classification and, by classical result of de Rham, also classification up to isometry.