Intersection cohomology of the circle actions

Abstract

A classical result says that a free action of the circle S 1 on a topological space X is geometrically classified by the orbit space B and by a cohomological class e ∈ H 2 ( B , Z ) , the Euler class. When the action is not free we have a difficult open question: ( Π ) “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.