Geometric Structures On 2orbifolds Exploration Of Discrete Symmetry Suhyoung Choi by Suhyoung Choi 9784931469686, 493146968X instant download after payment.

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.