Homotopy operations and rational homotopy type

David Blanc

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arXiv · math/0410075

Homotopy operations and rational homotopy type

David Blanc

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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\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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David Blanc. 2004-10-05. Homotopy operations and rational homotopy type. https://arxiv.org/abs/math/0410075

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