Homotopy operations and rational homotopy type

2004/10/05 by David Blanc
Mathematics · #math.AT #msc:55P62 #msc:55Q35 #msc:55P15 #msc:18G50

paper · pdf

published as "Algebraic Topology: categorical decomposition techniques", Progress in Mathematics 215 (2003), pp. 47-75 · 28 pages

arxiv created 2004/10/05 · arxiv updated 2009/12/01

Abstract

We describe a collection of higher homotopy operations which determine the rational homotopy type of a simply-connected space X. These are described in terms of simplicial resolutions of successive approximations (L^k,α to the Quillen DGL model for X. The operations lie in suitable cohomology groups H^*L^(k,α); π_* X⊗ Q of these DGLs. To facilitate the recovery of an integral version of the operations from the rational description, we also define a differential graded non-associative algebra model for rational spaces.

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