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Cohomology rings of almost-direct products of free groups

Part of: Connections with homological algebra and category theory Special aspects of infinite or finite groups Classical Topics in Algebraic Topology

Published online by Cambridge University Press:  22 January 2010

Daniel C. Cohen
Daniel C. Cohen*
Affiliation:
Department of Mathematics, Louisiana State University, Baton Rouge, LA 70803, USA (email: cohen@math.lsu.edu)
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Abstract

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An almost-direct product of free groups is an iterated semidirect product of finitely generated free groups in which the action of the constituent free groups on the homology of one another is trivial. We determine the structure of the cohomology ring of such a group. This is used to analyze the topological complexity of the associated Eilenberg–MacLane space.

Keywords

almost-direct productcohomology ringtopological complexity

MSC classification

Secondary: 20J06: Cohomology of groups 20F28: Automorphism groups of groups 20F36: Braid groups; Artin groups 55M30: Ljusternik-Schnirelman (Lyusternik-Shnirel'man) category of a space

Information

Type
Research Article
Information
Compositio Mathematica , Volume 146 , Issue 2 , March 2010 , pp. 465 - 479
Copyright
Copyright © Foundation Compositio Mathematica 2010

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