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arXiv · 2407.00189

Spin Link Homology

Elijah Bodish·Ben Elias·David E. V. Rose
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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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Elijah Bodish, Ben Elias, David E. V. Rose. 2024-06-28. Spin Link Homology. https://arxiv.org/abs/2407.00189

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