A classical theorem of Mac Lane and Whitehead states that the homotopy type of a topological space with trivial homotopy at dimensions 3 and greater can be reconstructed from its 711 and 712, and a cohomology class ks ~H~(rri, 7~). More recently, Moerdijk and Svensson suggested the possibility of using Bredon cohomology to extend this result to the equivariant case, that is, for spaces X equipp...

We present a simple proof of a precise version of the localization theorem in equivariant cohomology. As an application, we describe the cohomology algebra of any compact symplectic variety with a multiplicity-free action of a compact Lie group. This applies in particular to smooth, projective spherical varieties. 1 A precise version of the localization theorem Let X be a topological space with...

There is a natural way to deform Killing foliation with non-closed leaves, due Ghys and Haefliger--Salem, into closed foliation, i.e., whose leaves are all closed. Certain transverse geometric topological properties preserved under these deformations, as previously shown by the authors. For instance, basic Euler characteristic invariant. In this article we show that equivariant cohomology ring ...