Algebra/Topology seminar

Speaker: Juliet Cooke

Title: Skein Categories

Abstract: Skein algebras are classical invariants of surfaces based on considering ribbon graphs in thickened surfaces subject to some skein relations. In this talk I will describe my work fitting skein algebras within the framework of factorisation homology. To do this we shall consider a skein algebra as an endomorphism algebra in a certain category of coloured ribbon graphs called a skein category. We shall then see how these skein categories, unlike skein algebras, satisfy excision and therefore fit within the framework of factorisation homology as k-linear factorisation homology theories of surfaces. We shall conclude by discussing how this relates to stated skein algebras and Alekseev's moduli algebras.