Date: 03 Oct 2006

Resolutions and Poincaré duality for finite groups

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Abstract

This talk is a survey of some recent joint work with Jon Carlson on cohomology of finite groups. I shall describe how, for an arbitrary finite group G, one can produce an algebraic analogue of a free G-action on a product of spheres. If k is the field of coefficients, one can use this to build a resolution of k as a kG-module, which consists of a finite Poincaré duality piece and a polynomial piece. This resolution has the same rate of growth as the minimal resolution, but in general is not quite minimal. The deviation from minimality is measured by secondary operations in group cohomology expressible in terms of matric Massey products.