Rational String Topology

2004/06/29 by Yves Felix, Felix, Yves, Jean-Claude Thomas +3
Mathematics · #17A65 #17B55 #54N45 #55N33 #55P35 #81T30 #Algebraic Topology (math.AT) #FOS: Mathematics #math.AT #msc:17A65 #msc:17B55 #msc:54N45 #msc:55N33 #msc:55P35 #msc:81T30

paper · pdf · doi:10.48550/arxiv.math/0406593

arxiv created 2004/06/29 · arxiv updated 2009/12/01

Abstract

We use the computational power of rational homotopy theory to provide an explicit cochain model for the loop product and the string bracket of a 1-connected closed manifold M. We prove that the loop homology of M is isomorphic to the Hochschild cohomology of the commutative graded algebra A_PL(M) with coefficients in itself. Some explicit computations of the loop product and the string bracket are given.

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