Analytic and topological realizations of the invariant Thom-Smale complex

2023/11/17 by Zhuang Hao, Zhuang, Hao · 1 citation
Computer Science · Mathematics · #37D15 #58A14 #58J37 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2311.10417

openalex publication_date 2023/11/17 · openalex created_date 2023/11/21 · openalex updated_date 2026/07/28

Abstract

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.

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• Symplectic semi-characteristics

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