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Real homotopy theory of semi-algebraic sets
We complete the details of a theory outlined by Kontsevich and Soibelman that asso- ciates 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.