Let
T be a compact torus and
X be a a finite
T-CW complex (e.g. a compact
T-manifold). In earlier work, the second author introduced a functor which assigns to
X a so called GKM-sheaf
whose ring of global sections
is isomorphic to the equivariant cohomology
whenever
X is equivariantly formal (meaning that
is a free module over
... [Show full abstract] . In the current paper we prove more generally that if and only if is reflexive, and find a geometric interpretation of the higher cohomology for .