Sullivan-deRham theory for rational Alexander-Spanier cohomology. (English) Zbl 0556.55011
From the authors’ introduction: ”Equivariant rational cohomology theory as defined by A. Borel has proven to be a very useful tool in the study of torus group actions. The first author defined and developed an analogous equivariant rational homotopy theory functor by means of Sullivan’s theory of minimal models. A difficulty in this approach arises because Sullivan’s deRham theory is based upon singular cohomology whereas Borel’s equivariant theory is based upon Alexander-Spanier (or Čech or sheaf) cohomology. It is the purpose of this paper to show that one can avoid this difficulty by developing the Sullivan-deRham theory based on rational Alexander-Spanier cohomology and defining the equivariant rational homotopy functor accordingly.”
Reviewer: S.Jackowski
MSC:
55P62 | Rational homotopy theory |
57S17 | Finite transformation groups |
55N25 | Homology with local coefficients, equivariant cohomology |
55P91 | Equivariant homotopy theory in algebraic topology |
55N05 | Čech types |