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...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.展开更多
基金Supported by National Key R&D Program of China(Grant No.2020YFA0713300)NSFC(Grant Nos.11771303,12171327,11911530092,11871045)。
文摘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.
