Higher representations and cornered Heegaard Floer homology

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.

185 pages

References in corpus (2)

• Fivebranes and 3-manifold homology
• The Alexander polynomial as quantum invariant of links

Cited by in corpus (5)

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