Analytic and topological realizations of the invariant Thom-Smale complex

Hao Zhuang

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arXiv · 2311.10417

Analytic and topological realizations of the invariant Thom-Smale complex

Hao Zhuang

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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.

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Hao Zhuang. 2023-11-17. Analytic and topological realizations of the invariant Thom-Smale complex. https://arxiv.org/abs/2311.10417

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