Analytic and topological realizations of the invariant Thom-Smale complex
Zhuang Hao · arXiv (Cornell University) · 2023
With the smooth action of a connected compact Lie group $G$, we establish the chain isomorphism between the $G$-invariant Witten instanton complex and the $G$-invariant Thom-Smale complex, both of which are associated to a specific Morse-Bott function on a closed oriented $G$-manifold. This result includes the influence from the horizontal direction around the critical set, generalizing the strict Morse case.