This article is cited in 4 papers

Classical and quantum Teichmüller spaces

A. Yu. Vasiliev^a, A. G. Sergeev<sup>b

a</sup> University of Bergen, Norway
^b Steklov Mathematical Institute of the Russian Academy of Sciences

Abstract: Teichmüller theory is a ramified and rapidly developing area of mathematics which has multiple connections with other directions in the mathematical sciences and with their applications, first and foremost in mathematical physics. In this survey the main lines of development of this theory and its applications to string theory are presented in a historical context.
Bibliography: 128 titles.

Keywords: Teichmüller space, Riemann surface, modulus of a family of curves, quasiconformal map, quasisymmetric homeomorphism, Beltrami differential, universal Teichmüller space, non-commutative geometry, geometric quantization.

UDC: 517.545+517.548

MSC: Primary 30C62, 30F60, 32G15, 81S10, 81T30; Secondary 30C75, 30F10, 30F35

Received: 27.01.2013

DOI: 10.4213/rm9517

 English version: Russian Mathematical Surveys, 2013, 68:3, 435–502

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