Paper
Higher representations and cornered Heegaard Floer homology
Authors
Andrew Manion, Raphael Rouquier
Abstract
We develop the 2-representation theory of the odd one-dimensional super Lie algebra and show it controls the Heegaard-Floer theory of surfaces of Lipshitz, Ozsváth and Thurston. Our main tool is the construction of a tensor product for 2-representations. We show it corresponds to a gluing operation for surfaces, or the chord diagrams of arc decompositions. This provides an extension of Heegaard-Floer theory to dimension one, expanding the work of Douglas, Lipshitz and Manolescu.