Equivariant intersection cohomology of the circle actions

Circle actions on pseudomanifolds have been studied in Padilla and Saralegi-Aranguren (Topol Appl 154:2764-2770, 2007) by using intersection cohomology (see also Hector and Saralegi in Trans Am Math Soc 338:263-288, 1993). In this paper, we continue that study using a more powerful tool, the equivariant intersection cohomology (Brylinski in Equivariant intersection cohomology, American Mathematical Society, Providence, 1992; Joshua in Math Z 195:239-253, 1987). In this paper, we prove that the orbit space B and the Euler class of the action Phi: S-1 x X -> X determine both the equivariant intersection cohomology of the pseudomanifold X and its localization. We also construct a spectral sequence converging to the equivariant intersection cohomology of X whose third term is described in terms of the intersection cohomology of B.