Title: Pre-Calabi-Yau Algebras and string topology for manifolds with boundary
2015.06.19 |
Date | Fri 03 Jul |
Time | 13:00 — 13:45 |
Location | QGM lounge 1530-326 |
Abstract:
A Calabi-Yau (CY) algebra is an A_{∞} algebra with a certain kind of duality. An example is the de-Rham algebra of forms on a compact, closed, oriented manifold. A pre — CY (or V_{∞}) algebra is a generalization. We shall explain these notions and how the Hochschild chain compex of a 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 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.