Abstract
Recently R. Cohen and V. Godin have proved that the loop homology \(H_{\ast+m} (LM ; {\varvec k})\) of a closed oriented m dimensional manifold M with coefficients in a field k has the structure of a unital Frobenius algebra without counit. When the characteristic of k is zero we describe explicitly the dual of the coproduct \(H^{\ast} (LM ; {\varvec k})^{\otimes 2} \to H^{\ast+m} (LM ; {\varvec k})\) and prove that it respects the Hodge decomposition of \(H^{\ast}(LM ; {\varvec k})\).
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Chataur, D., Thomas, JC. Frobenius rational loop algebra. manuscripta math. 122, 305–319 (2007). https://doi.org/10.1007/s00229-006-0069-8
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DOI: https://doi.org/10.1007/s00229-006-0069-8