English

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.

Keywords

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

R2 v1 2026-06-21T10:46:54.655Z