Spin Link Homology

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