TITLE: Equivariant version of Morse theory
QUESTION [15 upvotes]: Is there some variant on Morse or Morse-Bott theory yielding equivariant (co)homology instead of singular homology?
Any reference/idea would be greatly appreciated.
Crossposted on StackExchange.

REPLY [4 votes]: If you like a Morse homological treatment, you could also look at the paper of Austin and Braam.

Austin, D. M.(1-IASP); Braam, P. J.(4-OX)
  Morse-Bott theory and equivariant cohomology. The Floer memorial volume, 123–183, 
  Progr. Math., 133, Birkhäuser, Basel, 1995.