Equivariant Morse-Bott cohomology through stabilization
Differential Geometry
2026-01-23 v1 Algebraic Topology
Dynamical Systems
Geometric Topology
Symplectic Geometry
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 -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.
Cite
@article{arxiv.2601.16119,
title = {Equivariant Morse-Bott cohomology through stabilization},
author = {Erkao Bao and Robi Huq and Shengzhen Ning},
journal= {arXiv preprint arXiv:2601.16119},
year = {2026}
}
Comments
26 pages, comments welcome!