  The Chang-Skjelbred method computes the cohomology of a suitable space with a
torus action from its equivariant one-skeleton. We show that, under certain
restrictions on the cohomological torsion, the integral cohomology is encoded
in the one-skeleton even in the presence of arbitrary disconnected isotropy
groups. We provide applications to Hamiltonian actions as well as to the GKM
case. In the latter, our results lead to a modification of the GKM formula for
graph cohomology.
