English

Analytic and topological realizations of the invariant Thom-Smale complex

Differential Geometry 2025-01-16 v4 Analysis of PDEs Dynamical Systems

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.

Keywords

Cite

@article{arxiv.2311.10417,
  title  = {Analytic and topological realizations of the invariant Thom-Smale complex},
  author = {Hao Zhuang},
  journal= {arXiv preprint arXiv:2311.10417},
  year   = {2025}
}

Comments

38 pages. More historical information, analytic details, and corollaries are added