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arxiv: math/0403100 · v5 · submitted 2004-03-04 · 🧮 math.AT · math.DG

Intersection cohomology of circle actions

classification 🧮 math.AT math.DG
keywords spaceclasseulerorbitactioncirclecohomologyfree
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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: $\Pi$ : "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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