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THE EULER CLASS OF A POINCARÉ DUALITY GROUP

Published online by Cambridge University Press:  17 June 2002

Ian J. Leary
Ian J. Leary
Affiliation:
Faculty of Mathematical Studies, University of Southampton, Southampton SO17 1BJ, UK ([email protected])
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Abstract

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Under an extra hypothesis satisfied in every known case, we show that the Euler class of an orientable odd-dimensional Poincaré duality group over any ring has order at most two. We construct groups that are of type FL over the complex numbers but are not FL over the rationals. We construct group algebras over fields for which $K_0$ contains torsion, and construct non-free stably free modules for the group algebras of certain virtually free groups.

AMS 2000 Mathematics subject classification: Primary 19A31. Secondary 16S34; 20J05; 55N15; 57P10

Keywords

group cohomologyPoincarédualityfiniteness conditions
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 45 , Issue 2 , June 2002 , pp. 421 - 448
Copyright
Copyright © Edinburgh Mathematical Society 2002