Geodesic
Real homotopy theory of semi-algebraic sets
Hardt, Robert1 ; Lambrechts, Pascal2 ; Turchin, Victor3 ; Volić, Ismar4
1Department of Mathematics, Rice University, 6100 S Main Street, MS 136, Houston TX 77005, USA
2Institut de Recherche en Mathématique et Physique, Chemin du cyclotron 2, B-1348 Louvain-la-Neuve, Belgium
3Department of Mathematics, Kansas State University, Manhattan, KS 66506, USA
4Mathematics Department, Wellesley College, 106 Central St, Wellesley MA 02481, USA
Algebraic and Geometric Topology, Tome 11 (2011) no. 5, pp. 2477-2545
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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 de Rham algebra of differential forms on a smooth manifold. Its development is needed for Kontsevich’s proof of the formality of the little cubes operad.

DOI : 10.2140/agt.2011.11.2477
Classification : 14P10, 55P62
Keywords: differential form, de Rham theory, semialgebraic set, rational homotopy theory

Hardt, Robert  1   ; Lambrechts, Pascal  2   ; Turchin, Victor  3   ; Volić, Ismar  4

1 Department of Mathematics, Rice University, 6100 S Main Street, MS 136, Houston TX 77005, USA
2 Institut de Recherche en Mathématique et Physique, Chemin du cyclotron 2, B-1348 Louvain-la-Neuve, Belgium
3 Department of Mathematics, Kansas State University, Manhattan, KS 66506, USA
4 Mathematics Department, Wellesley College, 106 Central St, Wellesley MA 02481, USA 
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Hardt, Robert; Lambrechts, Pascal; Turchin, Victor; Volić, Ismar. Real homotopy theory of semi-algebraic sets. Algebraic and Geometric Topology, Tome 11 (2011) no. 5, pp. 2477-2545. doi: 10.2140/agt.2011.11.2477

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