On the topology of locally volume collapsed Riemannian 3-orbifolds

Details On the topology of locally volume collapsed Riemannian 3-orbifolds On the topology of locally volume collapsed Riemannian 3-orbifolds

2011-01-19

arxiv.org/abs/1101.3644v1

Mathematics

Geometric Topology

62 pages

Scientific paper

We study the geometry and topology of Riemannian 3-orbifolds which are locally volume collapsed with respect to a curvature scale. We show that a sufficiently collapsed closed 3-orbifold without bad 2-suborbifolds either admits a metric of nonnegative sectional curvature or satisfies Thurston's Geometrization Conjecture. We also prove a version with boundary. Kleiner and Lott independently proved similar results.

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