A Weak∞-Functor in Morse Theory  

作　　者：Shan Zhong SUN Chen Xi WANG 

机构地区：[1]Department of Mathematics,Capital Normal University,Beijing,100048,P.R.China [2]Academy for Multidisciplinary Studies,Capital Normal University,Beijing,100048,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2024年第11期2571-2614,共44页数学学报（英文版）

基　　金：Supported by National Key R&D Program of China(Grant No.2020YFA0713300);NSFC(Grant Nos.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.

关 键 词：Morse function moduli space of gradient flow lines COMPACTIFICATIONS weak n/∞-category higher morphism HOMOTOPY 

分 类 号：O174[理学—数学]