Geometrization of Three-Dimensional Orbifolds via Ricci Flow

TL;DR

This paper provides a new, unified proof of the geometrization of three-dimensional closed orientable orbifolds using Ricci flow, complementing existing results with novel techniques and tools.

Contribution

It introduces a logically independent proof of orbifold geometrization via Ricci flow and develops new tools for orbifold geometry that could be of broader use.

Findings

Unified proof of orbifold geometrization using Ricci flow

Development of new geometric tools for orbifolds

Independent validation of existing decomposition results

Abstract

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.