An Introduction to Teichmüller SpacesThis 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. |
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A₂(H Ahlfors arbitrary assertion assume Aut(H base point Beltrami coefficient Beltrami differential Bers biholomorphic automorphism biholomorphic mapping canonical Chapter closed Riemann surface compact complex manifold complex structure conformal mapping converges Corollary corresponding curvature defined definition deformation denote ds² dzdy element equivalence class exists f₁ finite fixed points formula Fuchsian group Fuchsian model fundamental domain genus g half-plane H Hence holomorphic function homeomorphism homotopic hyperbolic length implies induced integral isomorphism Lemma locally uniformly mapping f mapping ƒ Math Möbius transformation moduli space nodes obtain p₁ Poincaré metric proof of Theorem Proposition quasiconformal mapping real-analytic respect satisfies self-mapping sequence simple closed geodesic subset surface of genus Teichmüller distance Teichmüller mapping Teichmüller space Teichmüller space T(R topology uniquely universal covering surface upper half-plane vector Weil-Petersson metric