2024/06/28 by Elijah Bodish, Bodish, Elijah, Ben Elias +3
Biochemistry, Genetics and Molecular Biology · Computer Science · Medicine · #17B37 #18N25 #57K18 #Advanced Electron Microscopy Techniques and Applications #Advanced Neuroimaging Techniques and Applications #FOS: Mathematics #Geometric Topology (math.GT) #Quantum Algebra (math.QA) #Representation Theory (math.RT) #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2407.00189
openalex publication_date 2024/06/28 · openalex created_date 2024/07/03 · openalex updated_date 2026/07/28
We put a new spin on Khovanov--Rozansky homology. That is, we equip Λn-colored \mathfraksl2n Khovanov--Rozansky homology with an involution whose ± 1-eigenspaces are link invariants. When n=1,2,3 (and assuming technical conjectures for n ≥ 4), we prove that this refined invariant categorifies the spin-colored \mathfrakso2n+1 quantum link polynomial. Along the way, we partially develop the theory of quantum \mathfrakso2n+1 webs and make contact with ιquantum groups.