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Frobenius Rational Loop Algebra


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.

Dates and versions

hal-00137922 , version 1 (22-03-2007)



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