The string coproduct/cobracket: A description over the reals and its homotopy invariance (Florian Naef, MIT)

16.06.2020 16:30 – 17:30

Given an orientable manifold M, Chas and Sullivan construct certain operations on the homology of the spaces of parameterized and unparameterized loops on M. These operations are given geometrically by intersecting families of loops and reconnecting them. Over the rationals one can identify the homology of the loop space and the unparameterized loop space with Hochschild and cyclic homology, respectively. We give two descriptions of the string coproduct/cobracket on the algebraic side, one in the simply-connected case using Poincaré duality models, and second one in the general case. Moreover, we construct a homotopy involutive Lie bialgebra structure on cyclic cochains extending the string cobracket that depends on the partition function of a Chern-Simons type field theory. Lastly, we discuss the (non-)homotopy invariance of that structure and its relation to the configuration space of two points.
This is joint work with Thomas Willwacher.

Lieu

Bâtiment: Battelle

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Séminaire "Groupes de Lie et espaces des modules"

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