Sergeev, Armen Quantization of universal Teichmüller space. (English) Zbl 1250.30042 Schlichenmaier, Martin (ed.) et al., Geometry and quantization. Lectures presented at the 3rd international school and conference, Geoquant, Luxembourg City, Luxembourg, August 31–September 5, 2009. Luxembourg: University of Luxembourg, Faculty of Science, Technology and Communication (ISBN 978-2-87971-079-2/pbk). Travaux Mathématiques 19, 7-26 (2011). The paper deals with the quantization of the universal Teichmüller space \(T=\text{QS}(S^1)/\text{Möb}(S^1)\), where \(\text{QS}(S^1)\) is the class of all quasisymmetric homeomorphisms of the unit circle \(S^1\), while \(\text{Möb}(S^1)\) is the the group of all Möbius transformations keeping \(S^1\) fixed. \(T\) contains the important space \(\text{Diff}_+(S^1)/\text{Möb}(S^1)\), where \(\text{Diff}_+(S^1)\) is the group of all smooth diffeomorphisms of \(S^1\). The author first describes the quantization of the subspace \(\text{Diff}_+(S^1)/\text{Möb}(S^1)\) by using the Dirac quantization. To discuss the whole universal Teichmüller space \(T\), the author uses an approach similar to the “quantized calculus” of Connes and Sullivan.For the entire collection see [Zbl 1222.53004]. Reviewer: Yuliang Shen (Suzhou) Cited in 2 Documents MSC: 30F60 Teichmüller theory for Riemann surfaces 32G15 Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables) Keywords:universal Teichmüller space; quantization PDFBibTeX XMLCite \textit{A. Sergeev}, Trav. Math. 19, 7--26 (2011; Zbl 1250.30042)