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Spin Link Homology

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arxiv 2407.00189 v1 pith:TTUI2B7O submitted 2024-06-28 math.QA math.GTmath.RT

Elijah Bodish , Ben Elias , David E. V. Rose This is my paper
classification math.QAmath.GTmath.RT
keywords homologylinkmathfrakquantumkhovanov--rozanskyspinalongassuming
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abstract

We put a new spin on Khovanov--Rozansky homology. That is, we equip $\Lambda^n$-colored $\mathfrak{sl}_{2n}$ Khovanov--Rozansky homology with an involution whose $\pm 1$-eigenspaces are link invariants. When $n=1,2,3$ (and assuming technical conjectures for $n \geq 4$), we prove that this refined invariant categorifies the spin-colored $\mathfrak{so}_{2n+1}$ quantum link polynomial. Along the way, we partially develop the theory of quantum $\mathfrak{so}_{2n+1}$ webs and make contact with $\iota$quantum groups.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Type $B$ Webs

    math.RT 2026-07 conditional novelty 7.0 of 10

    Type B webs give a complete diagrammatic presentation of the subcategory of U_q(so_{2n+1})-representations generated by the fundamental representations.

  2. Cyclic Sieving for Staircase Plane Partitions via Crystals and Electrical Networks

    math.CO 2026-07 conditional novelty 4.0 of 10

    Height-two staircase plane partitions satisfy cyclic sieving for promotion, proved by mapping promotion to rotation of 3-noncrossing perfect matchings via crystals and the electrical-network bush basis.

  3. Lectures on SL(3) foams and link homology

    math.QA 2025-07 conditional novelty 1.0 of 10

    This is an expository review of SL(3) foam evaluation and its use in categorifying the Kuperberg quantum invariant, with no new theorems.

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