Algebra/Topology Seminar 30/10/2020
Speaker: Lukas Woike
Title: Cyclic framed little disks algebras, Grothendieck-Verdier duality and handlebody group representations
Abstract: Associative and framed E_2-algebras in the category of categories (when considered up to coherent homotopy) are well-known to be equivalent to monoidal and balanced braided categories, respectively. However, both operads have a cyclic structure. In my talk, I will characterize cyclic algebras over both operads in a certain category of linear categories in terms of Grothendieck-Verdier duality in the sense of Boyarchenko-Drinfeld. When combined with Costello’s derived modular envelope construction, this leads to two applications in quantum topology: 1) A consistent system of handlebody group representations for any balanced braided Grothendieck-Verdier category generalizing the handlebody part of Lyubashenko's mapping class group actions. 2) A rigidity result for modular functors. This is joint work with Lukas Müller.