2025/05/19 by Dylan G. L. Allegretti, Allegretti, Dylan G. L., Hyun Kyu Kim +3
Mathematics · #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #Geometric Topology (math.GT) #Geometric and Algebraic Topology #High Energy Physics - Theory (hep-th) #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA) #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2505.13332
openalex publication_date 2025/05/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove a conjecture of the first and third named authors relating the Kauffman bracket skein algebra of a genus zero surface with boundary to a quantized K-theoretic Coulomb branch. As a consequence, we see that our skein algebra arises as the Grothendieck ring of the bounded derived category of equivariant coherent sheaves on the Braverman-Finkelberg-Nakajima variety of triples with monoidal structure defined by the convolution product. We thus give a monoidal categorification of the skein algebra, partially answering a question posed by D. Thurston.