  We show that the components, appearing in the decomposition theorem for
contraction maps of torus actions of complexity one, are intersection
cohomology complexes of even codimensional subvarieties. As a consequence, we
obtain the vanishing of the odd dimensional intersection cohomology for
rational complete varieties with torus action of complexity one. The article
also presents structural results on linear torus action in order to compute the
intersection cohomology from the weight matrix. In particular, we determine the
intersection cohomology Betti numbers of affine trinomial hypersurfaces in
terms of their defining equation.
