Circle actions on Kähler spaces (Q1313775)

The author studies an old problem in cohomology theory of transformation groups: ``If \(G = S^ 1\) or \(G = Z/p\) is acting on a Kähler manifold \(M\) with the fixed point set \(M^ G \neq \emptyset\), then each component of \(M^ G\) must resemble a Kähler manifold cohomologically'' [\textit{W. Browder}, Topology 27, No. 4, 459-472 (1988; Zbl 0669.57023)]. He gives an answer to this problem with an example of a semi-free circle group action on a cohomology Kähler manifold such that no component of the fixed point set is a cohomology Kähler manifold.