Volume 20, issue 1 (2016)

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Derived functors of the divided power functors

Lawrence Breen, Roman Mikhailov and Antoine Touzé

Geometry & Topology 20 (2016) 257–352

We study the derived functors of the components Γd(A) of the divided power algebra Γ(A) associated to an abelian group A, with special emphasis on the d = 4 case. While our results have applications both to representation theory and to algebraic topology, we illustrate them here by providing a new functorial description of certain integral homology groups of the Eilenberg–Mac Lane spaces K(A,n) for A a free abelian group. In particular, we give a complete functorial description of the groups H(K(A,3); ) for such A.

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strict polynomial functors, derived functors of non-additive functors, Eilenberg–Mac Lane spaces
Mathematical Subject Classification 2010
Primary: 18G55
Secondary: 55P20
Received: 28 February 2014
Revised: 29 January 2015
Accepted: 3 April 2015
Published: 29 February 2016
Proposed: Paul Goerss
Seconded: Ralph Cohen, Haynes Miller
Lawrence Breen
Université Paris 13
99, avenue Jean-Baptiste Clément
F-93430 Villetaneuse
Roman Mikhailov
Chebyshev Laboratory
St Petersburg State University
St Petersburg Department of Steklov Mathematical Institute
14th Line, 29b
Saint Petersburg
Antoine Touzé
Laboratoiré Paul Painlevé, CNRS (UMR 8524)
Université Lille 1
F-59000 Lille