John Rutter, University of Liverpool

Title: Groups of homotopyself-equivalences of lens spaces and of 2-dimensional
cellular models of combinatorially aspherical groups

Synopsis We define here the (2n+1)-dimensional lens spaces of
combinatorially aspherical presentations of groups. We calculate the group
of homotopy self-equivalence classes of these generalised lens spaces as a
semi-direct product and, up to group extension, of their even dimensional
skeleta, where the latter group extension is partially determined as a
semi-direct product in dimensions greater than 2 . The 2-skeleton of these
spaces is the cellular model of the presentation, and we obtain some
results on the group of homotopy self-equivalence classes of such cellular
models. We first calculate certain cohomology groups of combinatorially
aspherical groups  $\pi $  in a manner which enables us to calculate the
stabilisers of their elements under the actions of the automorphism groups
of  $\pi $ and of the coefficient groups.