The Group of Quasisymmetric Homeomorphisms of the Circle and Quantization of the Universal Teichmüller Space
| dc.creator | Sergeev, Armen G. | |
| dc.date | 2009-02-08 | |
| dc.date.accessioned | 2026-07-07T12:39:22Z | |
| dc.date.available | 2026-07-07T12:39:22Z | |
| dc.description | In the first part of the paper we describe the complex geometry of the universal Teichmüller space $\mathcal T$, which may be realized as an open subset in the complex Banach space of holomorphic quadratic differentials in the unit disc. The quotient $\mathcal S$ of the diffeomorphism group of the circle modulo Möbius transformations may be treated as a smooth part of $\mathcal T$. In the second part we consider the quantization of universal Teichmüller space $\mathcal T$. We explain first how to quantize the smooth part $\mathcal S$ by embedding it into a Hilbert-Schmidt Siegel disc. This quantization method, however, does not apply to the whole universal Teichmüller space $\mathcal T$, for its quantization we use an approach, due to Connes. | |
| dc.identifier | https://arxiv.org/abs/0902.1302 | |
| dc.identifier | http://arxiv.org/abs/0902.1302 | |
| dc.identifier | SIGMA 5 (2009), 015, 20 pages | |
| dc.identifier | doi:10.3842/SIGMA.2009.015 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/219084 | |
| dc.subject | Geometric Topology | |
| dc.subject | Complex Variables | |
| dc.subject | Quantum Algebra | |
| dc.title | The Group of Quasisymmetric Homeomorphisms of the Circle and Quantization of the Universal Teichmüller Space | |
| dc.type | text |