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Real homotopy theory of
semi-algebraic sets
Robert Hardt, Pascal Lambrechts, Victor Turchin and Ismar Volić |
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Algebraic & Geometric Topology 11 (2011) 2477–2545
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Abstract |
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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. |
Keywords
differential form, de Rham theory, semialgebraic set,
rational homotopy theory
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Mathematical Subject Classification 2010
Primary: 14P10, 55P62
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References |
Publication
Received: 27 January 2011
Accepted: 30 June 2011
Published: 13 September 2011
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Authors |
| Robert Hardt | |
| Department of Mathematics Rice University 6100 S Main Street MS 136 Houston TX 77005 USA |
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| http://math.rice.edu/~hardt | |
| Pascal Lambrechts | |
| Institut de Recherche en
Mathématique et Physique Chemin du cyclotron 2 B-1348 Louvain-la-Neuve Belgium |
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| http://milnor.math.ucl.ac.be/plwiki | |
| Victor Turchin | |
| Department of Mathematics Kansas State University Manhattan, KS 66506 USA |
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| http://www.math.ksu.edu/~turchin | |
| Ismar Volić | |
| Mathematics Department Wellesley College 106 Central St Wellesley MA 02481 USA |
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| http://palmer.wellesley.edu/~ivolic | |
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