2:00 pm Saturday, December 14, 2013
Back Porch Seminar : Factorization homology for surfaces by David Jordan (U. Edinburgh) in Schedler and Lawn's Back Porch
Note the address (sent in email). There will be quiche and beverages served! Abstract: Factorization homology is a gadget for constructing invariants of manifolds from algebraic data, or conversely, for organizing algebraic data topologically. Its main feature is a cut-and-paste axiom analogous to Mayer-Vietoris excision axiom for ordinary homology, which lets you compute the factorization homology of a manifold, given its decomposition into a union of submanifolds. So factorization homology provides especially amenable instances of "topological field theories", about which Sam talked last time on the back porch. In this talk, I'll introduce factorization homology, and explain a technique we developed with Ben-Zvi and Brochier, for computing the factorization homology of surfaces, by relating the cut-and-paste procedure to the Peter-Weyl decomposition for algebraic groups. As an application, we can compute explicitly the factorization homologies of any (compact, possibly punctured) surface, and relate them to several well-known constructions in representation theory, and some new ones. I'll explain any necessary background and give many examples in the first hour, at least in outline, so there are no prerequisites for coming along.
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