Vous êtes ici :  » Luc Menichi

Notes d’exposés

  • Sullivan models and free loop space :

A short introduction to Sullivan models, with the Sullivan model of a free loop space and the detailed proof of Vigué-Sullivan theorem on the Betti numbers of free loop space. Workshop on free loop space à Strasbourg, November 2008, scanned notes.

  • Cohomologie de Hochschild et Topologie des Cordes :

Exposé dans le cadre des Journées d’Algèbre "Dualité et structures BV en algèbre et en topologie", à Clermont-Ferrand, Juin 2009. résumé , notes scannées .

  • Topological Field theory on the Hochschild homology of a Calabi-Yau algebra :

Talk given at the workshop strings in Copenhagen, February 15-19, 2010. scanned notes taken by a participant.

Abstract : In our paper Batalin-Vilkovisky algebra structures on Hochschild Cohomology, we showed that the (dual of the) Hochschild homology of a Calabi-Yau algebra is a Batalin-Vilkovisky algebra. In On the Classification of Topological Field Theories, Jacob Lurie announced that the Hochschild homology of a Calabi-Yau algebra, more generally, has a structure of closed topological conformal field theory.

  • Eilenberg-Moore spectral sequence and string topology :

Talk given at the workshop algebraic homotopy and its applications, June 25-29, 2012. scanned notes . Extended talk given at the workshop String Topology and Related Topics, April 16, 2013. notes taken by Richard Hepworth.

Let $M$ be a simply-connected closed manifold. Chas and Sullivan have defined a product on the shifted homology of the free loop space $\mathbbH_*(LM)$. Consider over any field, the usual homological Eilenberg-Moore spectral sequence converging to $H_*(LM)$. Using results of F\’elix and Thomas, we show that this spectral sequence is multiplicative with respect to the Chas-Sullivan loop product and that its $E_2$-term is the Hochschild cohomology of $H^*(M)$. This gives a new method to compute the loop homology algebra of spheres and complex projective spaces. This is joint work with K. Kuribayashi and T. Naito.