Higher Structure Conferences Tanaka (Rev #1)

Factorization homology:

Invariants of modules and algebras as topological field theories

Abstract: Factorization homology is a way of constructing invariants of algebras, and of manifolds, at the same time. For instance, to an associative algebra and a circle, one associates the Hochschild homology of the algebra. These invariants are more sensitive to the manifold’s diffeomorphism class than usual homology (which is only sensitive to the manifold up to homotopy equivalence). Moreover, the invariants satisfy a local-to-global property similar to excision for singular homology–for instance, they satisfy a locality axiom that allows factorization homology to define a topological field theory. We’ll talk about how the factorization homology can be generalized to create invariants of algebras with modules (and manifolds with startifications) to create, for instance, link invariants. This is joint work with David Ayala and John Francis.