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Transactions of the American Mathematical Society

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The real cohomology of virtually nilpotent groups


Authors: Karel Dekimpe and Hannes Pouseele
Journal: Trans. Amer. Math. Soc. 359 (2007), 2539-2558
MSC (2000): Primary 20J06, 57T15
DOI: https://doi.org/10.1090/S0002-9947-07-04274-2
Published electronically: January 25, 2007
MathSciNet review: 2286044
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Abstract: In this paper we present a method to compute the real cohomology of any finitely generated virtually nilpotent group. The main ingredient in our setup consists of a polynomial crystallographic action of this group. As any finitely generated virtually nilpotent group admits such an action (which can be constructed quite easily), the approach we present applies to all these groups. Our main result is an algorithmic way of computing these cohomology spaces. As a first application, we prove a kind of Poincaré duality (also in the nontorsion free case) and we derive explicit formulas in the virtually abelian case.


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Additional Information

Karel Dekimpe
Affiliation: Katholieke Universiteit Leuven, Campus Kortrijk, B–8500 Kortrijk, Belgium

Hannes Pouseele
Affiliation: Katholieke Universiteit Leuven, Campus Kortrijk, B–8500 Kortrijk, Belgium
Address at time of publication: Gelÿkmeidstraat 12/2, B-8400 Oostende, Belgium

DOI: https://doi.org/10.1090/S0002-9947-07-04274-2
Received by editor(s): February 3, 2005
Published electronically: January 25, 2007
Additional Notes: The second author is a Research Assistant of the Fund for Scientific Research–Flanders (F.W.O.)
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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