An introduction to Teichmüller spaces

This book offers an easy and compact access to the theory of Teichm?ller spaces, starting from the most elementary aspects to the most recent developments, e.g. the role this theory plays with regard to string theory. Teichm?ller spaces give parametrization of all the complex structures on a given Riemann surface. This subject is related to many different areas of mathematics including complex analysis, algebraic geometry, differential geometry, topology in two and three dimensions, Kleinian and Fuchsian groups, automorphic forms, complex dynamics, and ergodic theory. Recently, Teichm?ller spaces have begun to play an important role in string theory. Imayoshi and Taniguchi have attempted to make the book as self-contained as possible. They present numerous examples and heuristic arguments in order to help the reader grasp the ideas of Teichm?ller theory. The book will be an excellent source of information for graduate students and reserachers in complex analysis and algebraic geometry as well as for theoretical physicists working in quantum theory. This book offers an easy and compact access to the theory of Teichmüller spaces, starting from the most elementary aspects to the most recent developments, e.g. the role this theory plays with regard to string theory. Teichmüller spaces give parametrization of all the complex structures on a given Riemann surface. This subject is related to many different areas of mathematics including complex analysis, algebraic geometry, differential geometry, topology in two and three dimensions, Kleinian and Fuchsian groups, automorphic forms, complex dynamics, and ergodic theory. Recently, Teichmüller spaces have begun to play an important role in string theory. Imayoshi and Taniguchi have attempted to make the book as self-contained as possible. They present numerous examples and heuristic arguments in order to help the reader grasp the ideas of Teichmüller theory. The book will be an excellent source of information for graduate students and researchers in complex analysis and algebraic geometry as well as for theoretical physicists working in quantum theory This introduction to the theory of Teichmuller spaces starts with some basic facts on Riemann surfaces the authors provide an overview of the subject and cover some very recent research topics. They have included heuristic arguments and numerous examples.