Geometrization of Three-Dimensional Orbifolds via Ricci Flow

Details Geometrization of Three-Dimensional Orbifolds via Ricci Flow Geometrization of Three-Dimensional Orbifolds via Ricci Flow

2011-01-19

arxiv.org/abs/1101.3733v2

Mathematics

Differential Geometry

20 figures

Scientific paper

A three-dimensional closed orientable orbifold (with no bad suborbifolds) is known to have a geometric decomposition from work of Perelman along with earlier work of Boileau-Leeb-Porti and Cooper-Hodgson-Kerckhoff. We give a new, logically independent, unified proof of the geometrization of orbifolds, using Ricci flow. Along the way we develop some tools for the geometry of orbifolds that may be of independent interest.

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