Rational String Topology

Details Rational String Topology Rational String Topology

2004-06-29

arxiv.org/abs/math/0406593v1

Mathematics

Algebraic Topology

Scientific paper

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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