The Complex Analytic Theory Of Teichmuller Spaces
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The Complex Analytic Theory of Teichmuller Spaces
An accessible, self-contained treatment of the complex structure of the Teichmüller moduli spaces of Riemann surfaces. Complex analysts, geometers, and especially string theorists (!) will find this work indispensable. The Teichmüller space, parametrizing all the various complex structures on a given surface, itself carries (in a completely natural way) the complex structure of a finite- or infinite-dimensional complex manifold. Nag emphasizes the Bers embedding of Teichmüller spaces and deals with various types of complex-analytic coördinates for them. This is the first book in which a complete exposition is given of the most basic fact that the Bers projection from Beltrami differentials onto Teichmüller space is a complex analytic submersion. The fundamental universal property enjoyed by Teichmüller space is given two proofs and the Bers complex boundary is examined to the point where totally degenerate Kleinian groups make their spectacular appearance. Contains much material previously unpublished.
Geometry of Riemann Surfaces and Teichmüller Spaces
The moduli problem is to describe the structure of the spaceof isomorphism classes of Riemann surfaces of a giventopological type. This space is known as the modulispace and has been at the center of pure mathematics formore than a hundred years. In spite of its age, this fieldstill attracts a lot of attention, the smooth compact Riemannsurfaces being simply complex projective algebraic curves.Therefore the moduli space of compact Riemann surfaces is alsothe moduli space of complex algebraic curves. This space lieson the intersection of many fields of mathematics and may bestudied from many different points of view.The aim of thismonograph is to present information about the structure of themoduli space using as concrete and elementary methods aspossible. This simple approach leads to a rich theory andopens a new way of treating the moduli problem, putting newlife into classical methods that were used in the study ofmoduli problems in the 1920s.
An Introduction to Teichmüller Spaces
Author: Yoichi Imayoshi
language: en
Publisher: Springer Science & Business Media
Release Date: 2012-12-06
This book offers an easy and compact access to the theory of TeichmA1/4ller spaces, starting from the most elementary aspects to the most recent developments, e.g. the role this theory plays with regard to string theory. TeichmA1/4ller 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, TeichmA1/4ller 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 TeichmA1/4ller 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.