Open Access
2011 Derived functors of nonadditive functors and homotopy theory
Lawrence Breen, Roman Mikhailov
Algebr. Geom. Topol. 11(1): 327-415 (2011). DOI: 10.2140/agt.2011.11.327


The main purpose of this paper is to extend our knowledge of the derived functors of certain basic nonadditive functors. The discussion takes place over the integers, and includes a functorial description of the derived functors of certain Lie functors, as well as that of the main cubical functors. We also present a functorial approach to the study of the homotopy groups of spheres and of Moore spaces M(A,n), based on the Curtis spectral sequence and the decomposition of Lie functors as iterates of simpler functors such as the symmetric or exterior algebra functors. As an illustration, we retrieve in a purely algebraic manner the 3–torsion components of the homotopy groups of the 2–sphere in low degrees, and give a unified presentation of the homotopy groups πi(M(A,n)) for small values of both i and n.


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Lawrence Breen. Roman Mikhailov. "Derived functors of nonadditive functors and homotopy theory." Algebr. Geom. Topol. 11 (1) 327 - 415, 2011.


Received: 18 January 2010; Accepted: 2 August 2010; Published: 2011
First available in Project Euclid: 19 December 2017

zbMATH: 1214.18012
MathSciNet: MR2764044
Digital Object Identifier: 10.2140/agt.2011.11.327

Primary: 18G10 , 18G55
Secondary: 54E30 , 55Q40

Keywords: Moore space , nonadditive derived functor

Rights: Copyright © 2011 Mathematical Sciences Publishers

Vol.11 • No. 1 • 2011
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