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Uspekhi Mat. Nauk, 2013, Volume 68, Issue 3(411), Pages 39–110 (Mi umn9517)  

This article is cited in 1 scientific paper (total in 1 paper)

Classical and quantum Teichmüller spaces

A. Yu. Vasilieva, A. G. Sergeevb

a 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.

Funding Agency Grant Number
Research Council of Norway 204726/V30
213440/BG
Russian Foundation for Basic Research 10-01-00178
11-01-12033-офи-м
Ministry of Education and Science of the Russian Federation НШ-7675.2010.1
Russian Academy of Sciences - Federal Agency for Scientific Organizations


DOI: https://doi.org/10.4213/rm9517

Full text: PDF file (1067 kB)
References: PDF file   HTML file

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

Bibliographic databases:

Document Type: Article
UDC: 517.545+517.548
MSC: Primary 30C62, 30F60, 32G15, 81S10, 81T30; Secondary 30C75, 30F10, 30F35
Received: 27.01.2013

Citation: A. Yu. Vasiliev, A. G. Sergeev, “Classical and quantum Teichmüller spaces”, Uspekhi Mat. Nauk, 68:3(411) (2013), 39–110; Russian Math. Surveys, 68:3 (2013), 435–502

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. G. Sergeev, “Quantization of the Sobolev space of half-differentiable functions”, Sb. Math., 207:10 (2016), 1450–1457  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
  • Успехи математических наук Russian Mathematical Surveys
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