Equivariant intersection cohomology of the circle actions

TL;DR

This paper establishes that the orbit space and Euler class fully determine the equivariant intersection cohomology of circle actions on pseudomanifolds, and introduces a spectral sequence linking these concepts.

Contribution

It provides a new method to compute equivariant intersection cohomology using the orbit space, Euler class, and a spectral sequence framework.

Findings

Orbit space and Euler class determine equivariant intersection cohomology.

Constructed a spectral sequence converging to the equivariant intersection cohomology.

Described the third term of the spectral sequence in terms of intersection cohomology of the orbit space.

Abstract

In this paper, we prove that the orbit space B and the Euler class of an action of the circle S^1 on 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.