The Complex Analytic Theory of Teichmuller SpacesAn 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 Contains much material previously unpublished. |
Contents
Introduction | 1 |
A Portmanteau of Preliminaries | 8 |
A Résumé of Results | 89 |
Copyright | |
7 other sections not shown
Common terms and phrases
action acts actually analytic arbitrary automorphism Banach space Beltrami differentials Bers biholomorphic boundary bounded bundle called canonical clearly compact complex manifold complex structure connected Consequently consider continuous convergence coordinates corresponding course covering curves defined definition derivative determined diffeomorphism differential dilatation dimension disk domain elements equation equivalent example Exercise exists fact fiber finite fixed follows formula Fuchsian group function fundamental genus g given gives group G Hence holomorphic homotopy hyperbolic identified identity induced integral isomorphism Lemma linear marked metric Möbius modular moduli natural neighborhood normalized Note obtained precisely projection proof Proposition prove punctures quasiconformal quasiconformal mappings Recall Remark represented respectively restricted Riemann surface Section simply smooth subgroup subset Teichmüller space theorem theory topological transformation trivial uniformizing unique universal vector zero