Mathematical Society of Japan Memoirs

Geometric Structures on 2-Orbifolds: Exploration of Discrete Symmetry

Suhyoung Choi

Book information

Suhyoung Choi

Publication information
MSJ Memoirs, Volume 27
Tokyo, Japan: The Mathematical Society of Japan, 2012
171 pp.

Publication date: 2012
First available in Project Euclid: 11 December 2014

Permanent link to this book

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Zentralblatt MATH:

Mathematical Reviews (MathSciNet):

Primary: 57M50: Geometric structures on low-dimensional manifolds 57S30: Discontinuous groups of transformations 20C99: None of the above, but in this section

Copyright © 2012, The Mathematical Society of Japan

Suhyoung Choi, Geometric Structures on 2-Orbifolds: Exploration of Discrete Symmetry (Tokyo: The Mathematical Society of Japan, 2012)


This book exposes the connection between the low-dimensional orbifold theory and geometry that was first discovered by Thurston in 1970s providing a key tool in his proof of the hyperbolization of Haken 3-manifolds. Our main aims are to explain most of the topology of orbifolds but to explain the geometric structure theory only for 2-dimensional orbifolds, including their Teichmüller (Fricke) spaces. We tried to collect the theory of orbifolds scattered in various literatures for our purposes. Here, we set out to write down the traditional approach to orbifolds using charts, and we include the categorical definition using groupoids. We will also maintain a collection of illustrative MathematicaTM packages at our homepages.