Equivariant intersection cohomology of the circle actions

Abstract

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 \(\Phi :{\mathbb{S }}^{1} \times X \rightarrow X\) 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 \(B\).