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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2024 MCQ for Transactions of the American Mathematical Society is 1.48 .

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The real cohomology of virtually nilpotent groups
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by Karel Dekimpe and Hannes Pouseele PDF
Trans. Amer. Math. Soc. 359 (2007), 2539-2558 Request permission

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
  • 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.)
  • © Copyright 2007 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • 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
  • MathSciNet review: 2286044