Homotopy operations and rational homotopy type

Details Homotopy operations and rational homotopy type Homotopy operations and rational homotopy type

2004-10-05

arxiv.org/abs/math/0410075v1

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

Mathematics

Algebraic Topology

28 pages

Scientific paper

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,\alpha} to the Quillen DGL model for X. The operations lie in suitable cohomology groups H^*{L^{(k,\alpha)}; \pi_* X\otimes 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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