Calcul d'algèbre de Frobenius sur l'homologie des lacets libres d'une variété.

Abstract : In 1999, M.Chas and D.Sullivan have constructed on the homology of free loop space of a manifold a BV-algebra structure. This was the begining of the String topology theory. In this thesis, we show the compatibility of the Serre spectral sequence to Gysin morphism of smooth finite codimensional embeddings between manifolds. Then, we use this technic to compute some examples of structures of string topology. We study essentially the “loop product” and the “loop coproduct” which provide the homology of free loop space of a manifold a stucture of Frobenius algebra without counit.
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Submitted on : Tuesday, February 26, 2008 - 3:46:58 PM
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Jean-François Le Borgne. Calcul d'algèbre de Frobenius sur l'homologie des lacets libres d'une variété.. Mathématiques [math]. Université d'Angers, 2006. Français. ⟨tel-00259066⟩

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