On the equivariant cohomology algebra for solenoidal actions

Abstract

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.

The cohomological structure of fixed point set for pro-torus actions on compactspaces

“…In this short paper, we shall prove this theorem for pro-torus actions on compact spaces. The theorem was generalized for solenoid ( 1-dimensional pro-torus) actions on compact spaces [20,Theorem 3.2]. Now let us recall the following theorem of Leray-Serre for fibrations, as given in [17,Theorem 5.2].…”