2023/09/12 by Tianyu Yuan, Yuan, Tianyu
Computer Science · Mathematics · #53D40 #58E05 #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric Topology (math.GT) #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA) #Symplectic Geometry (math.SG) #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2309.05976
openalex publication_date 2023/09/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present an approach to Morse theory on symmetric products of surfaces using the notion of folded ribbon trees. We introduce an A_∞-category with objects defined as κ-tuples of Morse functions, where the differential of the tuple has no self-intersection. We show that when the graph of the differential of the κ-tuple of Morse functions on T^*ℝ2 is the wrapped κ disjoint cotangent fibers, its endormorphism is the Hecke algebra associated to the symmetric group \mathfrakSκ.