2023/09/14 by Eilon Reisin-Tzur, Reisin-Tzur, Eilon
Mathematics · #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA) #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.2309.07824
openalex publication_date 2023/09/14 · openalex created_date 2023/09/16 · openalex updated_date 2026/07/28
We construct an isomorphism between the wrapped higher-dimensional Heegaard Floer homology of κ-tuples of cotangent fibers and κ-tuples of conormal bundles of homotopically nontrivial simple closed curves in T^*Σ with a certain braid skein group, where Σ is a closed oriented surface of genus > 0 and κ is a positive integer. Moreover, we show this produces a (right) module over the surface Hecke algebra associated to Σ. This module structure is shown to be equivalent to the polynomial representation of DAHA in the case where Σ=T2 and the cotangent fibers and conormal bundles of curves are both parallel copies.