Real Homotopy Theory of Semi-Algebraic Sets
Algebraic Topology
2014-10-01 v3 Algebraic Geometry
Abstract
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.
Cite
@article{arxiv.0806.0476,
title = {Real Homotopy Theory of Semi-Algebraic Sets},
author = {Robert Hardt and Pascal Lambrechts and Victor Tourtchine and Ismar Volic},
journal= {arXiv preprint arXiv:0806.0476},
year = {2014}
}
Comments
58 pages. Cosmetic changes with respect to previous version. Submitted