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arXiv · 2601.16119

Equivariant Morse-Bott cohomology through stabilization

Erkao Bao·Robi Huq·Shengzhen Ning
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Abstract

For closed manifolds with compact Lie group actions, we study Austin-Braam's Morse-theoretic construction of Borel equivariant cohomology using the technique of stabilization. We show that a $C^1$-small equivariant perturbation produces stable invariant Morse-Bott functions. This allows us to realize the equivariant transversality and orientability assumptions in Austin-Braam's framework by choosing generic invariant Riemannian metrics.

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BibTeXRIS

Erkao Bao, Robi Huq, Shengzhen Ning. 2026-01-22. Equivariant Morse-Bott cohomology through stabilization. https://arxiv.org/abs/2601.16119

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