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Frobenius Rational Loop Algebra

David Chataur·Jean-Claude Thomas
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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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David Chataur, Jean-Claude Thomas. 2005-03-07. Frobenius Rational Loop Algebra. https://arxiv.org/abs/math/0407014

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