Intersection cohomology of the circle actions

A classical result says that a free action of the circle S1 on a topological space X is geometrically classified by the orbit space B and by a cohomological class e∈H2(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.