2022/08/25 by Shanzhong Sun, Chenxi Wang, Sun, Shanzhong +1
Mathematics · Computer Science · #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2208.11959
In the spirit of Morse homology initiated by Witten and Floer, we construct two ∞-categories A and B. The weak one A comes out of the Morse-Samle pairs and their higher homotopies, and the strict one B concerns the chain complexes of the Morse functions. Based on the boundary structures of the compactified moduli space of gradient flow lines of Morse functions with parameters, we build up a weak ∞-functor F: A→ B. Higher algebraic structures behind Morse homology are revealed with the perspective of defects in topological quantum field theory.