Teichmüller Theory of Bordered Surfaces
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...
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| Дата: | 2007 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2007
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/147366 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Teichmüller Theory of Bordered Surfaces / L.O. Chekhov // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 23 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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irk-123456789-1473662019-02-15T01:24:35Z Teichmüller Theory of Bordered Surfaces Chekhov, L.O. 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 An and Dn algebras and discuss briefly the relation to the Thurston theory. 2007 Article Teichmüller Theory of Bordered Surfaces / L.O. Chekhov // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 23 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 37D40; 53C22 http://dspace.nbuv.gov.ua/handle/123456789/147366 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
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 An and Dn algebras and discuss briefly the relation to the Thurston theory. |
| format |
Article |
| author |
Chekhov, L.O. |
| spellingShingle |
Chekhov, L.O. Teichmüller Theory of Bordered Surfaces Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Chekhov, L.O. |
| author_sort |
Chekhov, L.O. |
| title |
Teichmüller Theory of Bordered Surfaces |
| title_short |
Teichmüller Theory of Bordered Surfaces |
| title_full |
Teichmüller Theory of Bordered Surfaces |
| title_fullStr |
Teichmüller Theory of Bordered Surfaces |
| title_full_unstemmed |
Teichmüller Theory of Bordered Surfaces |
| title_sort |
teichmüller theory of bordered surfaces |
| publisher |
Інститут математики НАН України |
| publishDate |
2007 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/147366 |
| citation_txt |
Teichmüller Theory of Bordered Surfaces / L.O. Chekhov // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 23 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT chekhovlo teichmullertheoryofborderedsurfaces |
| first_indexed |
2023-05-20T17:27:17Z |
| last_indexed |
2023-05-20T17:27:17Z |
| _version_ |
1796153328729587712 |