Higher representations and cornered Heegaard Floer homology

2020/09/21 by Manion, Andrew, Rouquier, Raphael · 1 citation
#FOS: Mathematics #Geometric Topology (math.GT) #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2009.09627

Abstract

We develop the 2-representation theory of the odd one-dimensional super Lie algebra gl(1|1)⁺ 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.

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• A categorification of representations of U_q(\mathfrakgl_1|1)

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