Appears in collections : Symplectic representation theory / Théorie symplectique des représentations, Exposés de recherche

Heegaard-Floer theory is a 4-dimensional topological fi theory. It has been partially extended down to dimension 2: Lipshitz-Oszvath-Thurston constructed a differential algebra for a surface equipped with some extra structure. Douglas and Manolescu started building a partial extension down to dimension 1. I will discuss joint work with Andy Manion where we explain a gluing mechanism for surfaces. This is based on the construction of a monoidal 2-category of 2-representations of $gl(1|1)^+$.