Mathematical Society of Japan Memoirs

Three-dimensional Orbifolds and Cone-Manifolds

Daryl Cooper, Craig D. Hodgson, and Steven P. Kerckhoff

Book information

Authors
Daryl Cooper, Craig D. Hodgson, and Steven P. Kerckhoff

Publication information
MSJ Memoirs, Volume 5
Tokyo, Japan: The Mathematical Society of Japan, 2000
178 pp.

Dates
Publication date: 2000
First available in Project Euclid: 17 January 2014

Permanent link to this book
https://projecteuclid.org/euclid.msjm/1389985812

Digital Object Identifier:
doi:10.2969/msjmemoirs/005010000

ISBN:
978-4-931469-05-1

Zentralblatt MATH:
0955.57014

Mathematical Reviews (MathSciNet):
MR1778789

Subjects
Primary: 57M50: Geometric structures on low-dimensional manifolds

Rights
Copyright © 2000, The Mathematical Society of Japan

Citation
Daryl Cooper, Craig D. Hodgson and Steven P. Kerckhoff, Three-dimensional Orbifolds and Cone-Manifolds (Tokyo: The Mathematical Society of Japan, 2000)

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Abstract

This volume provides an excellent introduction of the statement and main ideas in the proof of the orbifold theorem announced by Thurston in late 1981. It is based on the authors' lecture series entitled "Geometric Structures on 3-Dimensional Orbifolds" which was featured in the third MSJ Regional Workshop on "Cone-Manifolds and Hyperbolic Geometry" held on July 1-10, 1998, at Tokyo Institute of Technology. The orbifold theorem shows the existence of geometric structures on many 3-orbifolds and on 3-manifolds with symmetry. The authors develop the basic properties of orbifolds and cone-manifolds, extends many ideas from the differential geometry to the setting of cone-manifolds and outlines a proof of the orbifold theorem.