Intersection cohomology of circle actions

Details Intersection cohomology of circle actions Intersection cohomology of circle actions

2004-03-04

arxiv.org/abs/math/0403100v5

Topology and its Applications 254(2007), 2764-2770

Mathematics

Algebraic Topology

Scientific paper

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 $X$.

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