Rational string topology
(2007) Journal of the European Mathematical Society — Vol. 9, n° 1, p. 123-156 (2007)
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- 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 simply connected closed manifold M. We prove that the loop homology of M is isomorphic to the Hochschild cohomology of the cochain algebra C*(M) with coefficients in C*( M). Some explicit computations of the loop product and the string bracket are given.
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Félix, Y., Thomas, J.-C., & Vigue-Poirrier, M. (2007). Rational string topology. Journal of the European Mathematical Society, 9(1), 123-156. https://hdl.handle.net/2078.5/88210 (Original work published 2007)