Intersection cohomology of circle actions

Abstract

A classical result says that a free action of the circle ${\mathbb{S}}^1$ on a topological space $X$ is geometrically classified by the orbit space $B$ and by a cohomological class $H^{{}^2}(B,\mathbb{Z})$, the Euler class. When the action is not free we have a difficult open question: $\Pi$ : "Is the space $X$ determined by the orbit space $B$ and the Euler class?" The main result of this work is a step towards the understanding of the above question in the category of unfolded pseudomanifolds. We prove that the orbit space $B$ and the Euler class determine: * the intersection cohomology of $X$, * the real homotopy type of $X$.