Spin Link Homology Article Swipe

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Link (geometry) Spin (aerodynamics) Homology (biology) Physics Condensed matter physics Mathematics Genetics Biology Combinatorics Gene Thermodynamics

Elijah Bodish , Ben Elias , David E. V. Rose ·

YOU? · · 2024 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2407.00189 · OA: W4400267153

We put a new spin on Khovanov--Rozansky homology. That is, we equip $Λ^n$-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 $ι$quantum groups.