Title: Wheeled PROP structure on stable cohomology
Abstract: Wheeled PROPs, introduced by Markl, Merkulov and Shadrin are PROPs equipped with extra structures which can treat traces.
In this talk, after explaining the notions of PROPs and wheeled PROPs, I will describe a wheeled PROP structure on stable cohomology of automorphism groups of free groups with some particular coefficients. I will explain how cohomology classes constructed previously by Kawazumi can be interpreted using this wheeled PROP structure and I will construct a morphism of wheeled PROPs from a PROP given in terms of functor homology and the wheeled PROP evoked previously.
This is joint work with Nariya Kawazumi.