02679nam a22003495a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001600168084002200184100002900206245008500235260008200320300003400402336002600436337002600462338003600488347002400524490006100548506006600609520143100675650004502106650004802151650003102199856003202230856006702262183-140812CH-001817-320140812234500.0a fot ||| 0|cr nn mmmmamaa140812e20140812sz fot ||| 0|eng d a978303719641070a10.4171/1412doi ach0018173 7aPBK2bicssc a58-xxa53-xx2msc1 aSergeev, Armen,eauthor.10aLectures on Universal Teichmüller Spaceh[electronic resource] /cArmen Sergeev3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2014 a1 online resource (111 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Series of Lectures in Mathematics (ELM) ;x2523-51761 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php 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.07aCalculus & mathematical analysis2bicssc07aGlobal analysis, analysis on manifolds2msc07aDifferential geometry2msc40uhttps://doi.org/10.4171/141423cover imageuhttps://www.ems-ph.org/img/books/sergeev_mini.gif