Analytic and topological realizations of the invariant Thom-Smale complex

Abstract

With the smooth action of a connected compact Lie group G, we realize the G-invariant Thom-Smale complex in an analytic way using the G-invariant Witten instanton complex. Both complexes 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.