Rational String Topology
Algebraic Topology
2007-05-23 v1
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.
Cite
@article{arxiv.math/0406593,
title = {Rational String Topology},
author = {Yves Felix and Jean-Claude Thomas and Micheline Vigue-Poirrier},
journal= {arXiv preprint arXiv:math/0406593},
year = {2007}
}