Intersection cohomology of circle actions
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A classical result says that a free action of the circle $\Bbb{S}^1$ on a topological space $X$ is geometrically classified by the orbit space $B$ and by a cohomological class ${H}^{^{2}}{(B,\Bbb{Z})}$, 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 $X$.