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Frobenius Rational Loop Algebra

Abstract : Recently R. Cohen and V. Godin have proved that the homology of the free loop space of a closed oriented manifold with coefficients in a field has the structure of a Frobenius algebra without counit. In this short note we prove that when the characteristic of the field is zero and when the manifold is 1-connected the algebraic structure depends only on the rational homotopy type of the manifold. We build an algebraic model and use it to do some computations.
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Preprints, Working Papers, ...
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https://hal.archives-ouvertes.fr/hal-00137922
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Submitted on : Thursday, March 22, 2007 - 3:15:43 PM
Last modification on : Wednesday, October 20, 2021 - 3:18:44 AM

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David Chataur, Jean-Claude Thomas. Frobenius Rational Loop Algebra. 2005. ⟨hal-00137922⟩

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