## The complex analytic theory of Teichmüller spacesAn accessible, self-contained treatment of the complex structure of the Teichm?ller moduli spaces of Riemann surfaces. Complex analysts, geometers, and especially string theorists (!) will find this work indispensable. The Teichm?ller 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 Teichm?ller spaces and deals with various types of complex-analytic co?rdinates 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 Teichm?ller space is a complex analytic submersion. The fundamental universal property enjoyed by Teichm?ller 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 Contains much material previously unpublished. |

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### Contents

Introduction | 1 |

A Portmanteau of Preliminaries | 8 |

A Resume of Results | 89 |

Copyright | |

7 other sections not shown

### Common terms and phrases

Ahlfors Aq(D arbitrary Fuchsian group Banach manifold Banach space Beltrami differentials Bers projection biholomorphic automorphism boundary bundle canonical coefficients compact Riemann surface complex analytic complex Banach complex dilatation complex manifold complex structure convergence corresponding course defined definition derivative diffeomorphism disk domain elements embedding equation fact fiber space finite conformal type finite-dimensional fixed points Fuchsian group genus g given group G Hence holomorphic family holomorphic function holomorphic map holomorphic submersion homeomorphism homotopy hyperbolic identified identity induced integral isometry isomorphism Kleinian group Lemma linear M6bius transformation meromorphic function metric Mob(C Mod(G modular group moduli space morphism neighborhood normalized Note parameters Poincare Poincare metric precisely proof properly discontinuously Proposition prove punctures quadratic differentials quasicircle quasiconformal homeomorphism quasiconformal mappings quotient real-analytic Remark Riemannian schlicht self-homeomorphism subgroup subset subspace tangent Teichmiiller Teichmuller space Teichmuller's theorem topological torsion-free Fuchsian group trivial type g unique universal covering zero