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Эта публикация цитируется в 13 научных статьях (всего в 13 статьях)
Teichmüller Theory of Bordered Surfaces
Leonid O. Chekhovabcd a Institute for Theoretical and Experimental Physics, Moscow, Russia
b Steklov Mathematical Institute, Moscow, Russia
c Poncelet Laboratoire International Franco-Russe, Moscow, Russia
d Concordia University, Montréal, Quebec, Canada
Аннотация:
We propose the graph description of Teichmüller theory of surfaces with marked points on boundary components (bordered surfaces). Introducing new parameters, we formulate this theory in terms of hyperbolic geometry. We can then describe both classical and quantum theories having the proper number of Thurston variables (foliation-shear coordinates), mapping-class group invariance (both classical and quantum), Poisson and quantum algebra of geodesic functions, and classical and quantum braid-group relations. These new algebras can be defined on the double of the corresponding graph related (in a novel way) to a double of the Riemann surface (which is a Riemann surface with holes, not a smooth Riemann surface). We enlarge the mapping class group allowing transformations relating different Teichmüller spaces of bordered surfaces of the same genus, same number of boundary components, and same total number of marked points but with arbitrary distributions of marked points among the boundary components. We describe the classical and quantum algebras and braid group relations for particular sets of geodesic functions corresponding to $A_n$ and $D_n$ algebras and discuss briefly the relation to the Thurston theory.
Ключевые слова:
graph description of Teichmüller spaces; hyperbolic geometry; algebra of geodesic functions.
Поступила: 5 января 2007 г.; в окончательном варианте 28 апреля 2007 г.; опубликована 15 мая 2007 г.
Образец цитирования:
Leonid O. Chekhov, “Teichmüller Theory of Bordered Surfaces”, SIGMA, 3 (2007), 066, 37 pp.
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/sigma192 https://www.mathnet.ru/rus/sigma/v3/p66
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