论文标题
薄弱
A Weak $\infty$-Functor in Morse Theory
论文作者
论文摘要
本着Witten和Floer发起的Morse同源性的精神，我们构造了两个$ \ infty $-类别$ \ Mathcal {a} $和$ \ Mathcal {B} $。一个弱的$ \ MATHCAL {a} $来自摩尔斯纱对及其更高的同型，而严格的一个$ \ Mathcal {b} $涉及Morse功能的链条络合物。基于带有参数的梯度流量线的压实模量空间的边界结构，我们构建了一个弱$ \ infty $ functor $ \ mathcal {f}：\ Mathcal {a} \ rightarrow \ rightArrow \ Mathcal \ Mathcal {b} $。莫尔斯同源性背后的较高代数结构以拓扑量子场理论缺陷的视角揭示。
In the spirit of Morse homology initiated by Witten and Floer, we construct two $\infty$-categories $\mathcal{A}$ and $\mathcal{B}$. The weak one $\mathcal{A}$ comes out of the Morse-Samle pairs and their higher homotopies, and the strict one $\mathcal{B}$ 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 $\infty$-functor $\mathcal{F}: \mathcal{A}\rightarrow \mathcal{B}$. Higher algebraic structures behind Morse homology are revealed with the perspective of defects in topological quantum field theory.
