Real Homotopy Theory of Semi-Algebraic Sets

Details Real Homotopy Theory of Semi-Algebraic Sets Real Homotopy Theory of Semi-Algebraic Sets

2008-06-03

arxiv.org/abs/0806.0476v3

Mathematics

Algebraic Topology

58 pages. Cosmetic changes with respect to previous version. Submitted

Scientific paper

We complete the details of a theory outlined by Kontsevich and Soibelman that associates to a semi-algebraic set a certain graded commutative differential algebra of "semi-algebraic differential forms" in a functorial way. This algebra encodes the real homotopy type of the semi-algebraic set in the spirit of the DeRham algebra of differential forms on a smooth manifold. Its development is needed for Kontsevich's proof of the formality of the little cubes operad.

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