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arxiv: 1702.04140 · v3 · pith:CSSK5T4Nnew · submitted 2017-02-14 · 🧮 math.QA · math.GT

A closed formula for the evaluation of mathfrak{sl}_N-foams

Louis-Hadrien Robert , Emmanuel Wagner This is my paper
classification 🧮 math.QA math.GT
keywords mathfrakclosedequivariantevaluationfoamsformulaintegrallink
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We give a purely combinatorial formula for evaluating closed decorated foams. Our evaluation gives an integral polynomial and is directly connected to an integral equivariant version of the $\mathfrak{sl}_N$ link homology categorifying the $\mathfrak{sl}_N$ link polynomial. We also provide connections to the equivariant cohomology rings of partial flag manifolds.

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  1. Action of the Witt algebra on categorified quantum groups

    math.QA 2025-07 unverdicted novelty 6.0

    Constructs an action of the positive Witt algebra on categorified quantum groups for simply-laced Lie algebras, recovering the foam action in type A and inducing the current-algebra action via trace decategorification.