Derived functors of nonadditive functors and homotopy theory

Breen, Lawrence¹ ; Mikhailov, Roman²

¹Laboratoire CNRS LAGA, Universite Paris 13, 99, avenue Jean-Baptiste Clement, 93430 Villetaneuse, France
²Department of Algebra, Steklov Mathematical Institute, Gubkina 8, Moscow, 119991, Russia

Algebraic and Geometric Topology, Tome 11 (2011) no. 1, pp. 327-415

Résumé

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.

Détail

DOI : 10.2140/agt.2011.11.327

Keywords: nonadditive derived functor, Moore space

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