Geometric Structures on 2-Orbifolds: Exploration of Discrete Symmetry (Mathematical Society of Japan
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Yayıncı Mathematical Association of America ( 08 / 2012 ) ISBN 9784931469686 | 17,27x24,89x1,02 cm. | İngilizce | 171 Sayfa | Türler Matematik-İstatistik
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 Teichmuller (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.