On the topology of G-manifolds with finitely many non-principal orbits

Details On the topology of G-manifolds with finitely many non-principal orbits On the topology of G-manifolds with finitely many non-principal orbits

2011-06-17

arxiv.org/abs/1106.3432v1

Mathematics

Differential Geometry

15 pages

Scientific paper

We study the topology of compact manifolds with a Lie group action for which there are only finitely many non-principal orbits, and describe the possible orbit spaces which can occur. If some non-principal orbit is singular, we show that the Lie group action must have odd cohomogeneity. We pay special attention to manifolds with one and two singular orbits, and construct some infinite families of examples. To illustrate the diversity within some of these families, we also investigate homotopy types.

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