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Date:
03 Oct 2006
Resolutions and Poincaré duality for finite groups
 D. J. Benson
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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 Gaction on a product of spheres. If k is the field of coefficients, one can use this to build a resolution of k as a kGmodule, 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.
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 Title
 Resolutions and Poincaré duality for finite groups
 Book Title
 Algebraic Topology Homotopy and Group Cohomology
 Book Subtitle
 Proceedings of the 1990 Barcelona Conference on Algebraic Topology, held in S. Feliu de Guíxols, Spain, June 6–12, 1990
 Pages
 pp 1019
 Copyright
 1992
 DOI
 10.1007/BFb0087497
 Print ISBN
 9783540551959
 Online ISBN
 9783540467724
 Series Title
 Lecture Notes in Mathematics
 Series Volume
 1509
 Series ISSN
 00758434
 Publisher
 Springer Berlin Heidelberg
 Copyright Holder
 SpringerVerlag
 Additional Links
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 Editors
 Authors

 D. J. Benson ^{(1)}
 Author Affiliations

 1. Mathematical Institute, 2429 St. Giles, OX1 3LB, Oxford, Great Britain
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