Thurston's Orbifold Theorem
by
Daryl Cooper
UCSB
Coauthors: S. Kerckhoff, C. Hodgson

We discuss a proof of the orbifold theorem in the case that the singular locus is a 1-manifold. The proof is to study a deformation through hyperbolic metrics with cone singularities such that the cone angles around the meridians of the singular locus increase. If it happens that the diameter goes to zero one rescales the metric. Thus one studies constant curvature metrics of curvature between -1 and 0. The heart of the proof is to analyse such a metric when the injectivity radius is small everywhere. This is analogous to the Cheeger-Gromov study of F-structures. Using Euclidean "local models" a geometric/topological construction is given that produces an orbifold version of a graph-manifold or bundle structure.

Date received: December 17, 1998

Copyright © 1998 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caca-02.