# Pre-Calabi-Yau algebras and string topology for manifolds with boundary

Yiannis Vlassopoulos
(IHÉS)
Seminar
Fredag, 3 juli, 2015, at 13:00-13:45, QGM Staff lounge 1530-326
Abstrakt:

A Calabi-Yau ($CY$) algebra is an $A^\infty$ algebra with a certain kind of duality. An example is the de-Rham algebra of forms on a compact, closed, oriented manifold. A $\mathrm{pre-}CY$> (or $V^\infty$) algebra is a generalization. We shall explain these notions and how the Hochschild chain compex of a $\mathrm{pre-}CY$ algebra has the structure of an algebra over a dg-PROP $P$ of chains in the moduli space of Riemann surfaces with incoming and outgoing marked points. We will then show that the de-Rham algebra of forms on a manifold with boundary has the structure of a $\mathrm{pre-}CY$ algebra. If the manifold is simply connected this implies that the cohomology of its free loop space has the structure of an algebra over the dg-PROP $P$ and this can be thought of as a version of string topology for manifolds with boundary.

This is joint work with Maxim Kontsevich.

Organiseret af: QGM
Kontaktperson: Jørgen Ellegaard Andersen