A Weak ∞-Functor in Morse Theory

作     者：Shanzhong SUN Chenxi WANG 

作者机构：Department of Mathematics Capital Normal University Academy for Multidisciplinary Studies Capital Normal University 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报(英文版))

年 卷 期：2023年

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：Supported by National Key R&D Program of China (2020YFA0713300) NSFC (No.s 11771303, 12171327, 11911530092, 11871045) 

摘      要：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-Smale 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.