Mathematical Society of Japan Memoirs

Geometric Structures on 2-Orbifolds: Exploration of Discrete Symmetry

Suhyoung Choi

Book information

Author
Suhyoung Choi

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

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

Permanent link to this book
https://projecteuclid.org/euclid.msjm/1418313992

Digital Object Identifier:
doi:10.2969/msjmemoirs/027010000

ISBN:
978-4-931469-68-6

Zentralblatt MATH:
1260.57043

Mathematical Reviews (MathSciNet):
MR2962023

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

Rights
Copyright © 2012, The Mathematical Society of Japan

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

Abstract

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.