The argument that I used to prove the constancy of the homolomorphic Lefschetz number in a circle action has played some role in:

M.F.Atiyah,F.Hirzebruch, Spin manifolds and group actions, Essays on topology and related topics (memoires d\'edi\'es a
G.De Rham) 1970, Springer, New York,

where there is a reference to my result (but not to the paper itself). There is a similar reference in:

R.Bott,C.Taubes, On the rigidity theorem of Witten, Jour.Amer.Math.Soc. 2(1989).