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Equivariant Morse-Bott cohomology through stabilization

Published 22 Jan 2026 in math.DG, math.AT, math.DS, math.GT, and math.SG | (2601.16119v1)

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 $C1$-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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Authors (3)

  1. Erkao Bao 
  2. Robi Huq 
  3. Shengzhen Ning 

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