English

Intersection cohomology of circle actions

Algebraic Topology 2009-03-24 v5 Differential Geometry

Abstract

A classical result says that a free action of the circle S1\Bbb{S}^1 on a topological space XX is geometrically classified by the orbit space BB and by a cohomological class H2(B,Z){H}^{^{2}}{(B,\Bbb{Z})}, the Euler class. When the action is not free we have a difficult open question: Π\Pi : "Is the space XX determined by the orbit space BB 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 BB and the Euler class determine: * the intersection cohomology of XX, * the real homotopy type of XX.

Keywords

Cite

@article{arxiv.math/0403100,
  title  = {Intersection cohomology of circle actions},
  author = {Gabriel Padilla and Martintxo Saralegi-Aranguren},
  journal= {arXiv preprint arXiv:math/0403100},
  year   = {2009}
}
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