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020			_a9783037196410
024	7	0	_a10.4171/141 _2doi
040			_ach0018173
072		7	_aPBK _2bicssc
084			_a58-xx _a53-xx _2msc
100	1		_aSergeev, Armen, _eauthor.
245	1	0	_aLectures on Universal Teichmüller Space _h[electronic resource] / _cArmen Sergeev
260	3		_aZuerich, Switzerland : _bEuropean Mathematical Society Publishing House, _c2014
264		1	_aZuerich, Switzerland : _bEuropean Mathematical Society Publishing House, _c2014
300			_a1 online resource (111 pages)
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	0		_aEMS Series of Lectures in Mathematics (ELM)
506	1		_aRestricted to subscribers: _uhttp://www.ems-ph.org/ebooks.php
520			_aThis book is based on a lecture course given by the author at the Educational Center of Steklov Mathematical Institute in 2011. It is designed for a one semester course for undergraduate students, familiar with basic differential geometry, complex and functional analysis. The universal Teichmüller space $\mathcal T$ is the quotient of the space of quasisymmetric homeomorphisms of the unit circle modulo Möbius transformations. The first part of the book is devoted to the study of geometric and analytic properties of $\mathcal T$. It is an infinite-dimensional Kähler manifold which contains all classical Teichmüller spaces of compact Riemann surfaces as complex submanifolds which explains the name “universal Teichmüller space”. Apart from classical Teichmüller spaces, $\mathcal T$ contains the space $\mathcal S$ of diffeomorphisms of the circle modulo Möbius transformations. The latter space plays an important role in the quantization of the theory of smooth strings. The quantization of $\mathcal T$ is presented in the second part of the book. In contrast with the case of diffeomorphism space $\mathcal S$, which can be quantized in frames of the conventional Dirac scheme, the quantization of $\mathcal T$ requires an absolutely different approach based on the noncommutative geometry methods. The book concludes with a list of 24 problems and exercises which can be used during the examinations.
650	0	7	_aCalculus & mathematical analysis _2bicssc
650	0	7	_aGlobal analysis, analysis on manifolds _2msc
650	0	7	_aDifferential geometry _2msc
700	1		_aSergeev, Armen, _eauthor.
856	4	0	_uhttps://doi.org/10.4171/141
856	4	2	_3cover image _uhttp://www.ems-ph.org/img/books/sergeev_mini.gif
942			_2EBK13851 _cEBK
999			_c50475 _d50475