We prove, under certain conditions, that if a solenoidal group (i.e. 1-dimensional compact connected abelian group) acts effectively on a compact space then the fixed point set is nonempty and H_G^*(X,Q) has a presentation similar to the presentation of H^*(X,Q) as proven by Chang in the case of a circle group.
ÖZKURT, ALİ ARSLAN
"On the equivariant cohomology algebra for solenoidal actions,"
Turkish Journal of Mathematics: Vol. 38:
6, Article 11.
Available at: https://journals.tubitak.gov.tr/math/vol38/iss6/11