Intersection cohomology of circle actions
  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:   $\Pi$ : "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 $X$. 
Gabriel Padilla and Martintxo Saralegi-Aranguren