Topology seminar @ Stockholm University & KTH
- Title
- Plethysm for colored operads and prop(erad)s.
- Event
- Topology seminar.
- Location
- Stockholm University & KTH.
- On
- On .
- Related work
- Related work.
- Notes
- Notes.
Abstract
An operad is a symmetric sequence (or species) equipped with a monoid structure for the composition product. In characteristic zero, the data of a symmetric sequence is equivalent to that of its character, which is a symmetric function; the plethysm of two symmetric functions then corresponds to the composition product of the associated symmetric sequences.
In this talk I will explain how to define analogues of plethysm for various decategorifications of operadic structures: colored operads, props, and properads. These analogues admit a computable description and allow, among other things, determining the decomposition into irreducible factors of the twisted stable homology of automorphism groups of free groups, as well as the Albanese cohomology of IA automorphism groups.
(Work in collaboration with Erik Lindell.)