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The real cohomology of virtually nilpotent groups
Author(s):
Karel
Dekimpe;
Hannes
Pouseele
Journal:
Trans. Amer. Math. Soc.
359
(2007),
2539-2558.
MSC (2000):
Primary 20J06, 57T15
Posted:
January 25, 2007
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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:
Gelykmeidstraat 12/2, B-8400 Oostende, Belgium
DOI:
10.1090/S0002-9947-07-04274-2
PII:
S 0002-9947(07)04274-2
Received by editor(s):
February 3, 2005
Posted:
January 25, 2007
Additional Notes:
The second author is a Research Assistant of the Fund for Scientific Research--Flanders (F.W.O.)
Copyright of article:
Copyright
2007,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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