An algebraic characterization of simple closed curves on surfaces with boundary
We prove that a conjugacy class in the fundamental group of a surface with boundary is represented by a power of a simple curve if and only if the Goldman bracket of two different powers of this class, one of them larger than two, is zero. The main theorem actually counts self-intersection number of...
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todo:paper_17935253_v2_n3_p395_Chas2023-10-03T16:32:54Z An algebraic characterization of simple closed curves on surfaces with boundary Chas, M. Krongold, F. conjugacy classes embedded curves hyperbolic geometry intersection number Lie algebras Surfaces We prove that a conjugacy class in the fundamental group of a surface with boundary is represented by a power of a simple curve if and only if the Goldman bracket of two different powers of this class, one of them larger than two, is zero. The main theorem actually counts self-intersection number of a primitive class by counting the number of terms of the Goldman bracket of two distinct powers, one of them larger than two. © 2010 World Scientific Publishing Company. Fil:Chas, M. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Krongold, F. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_17935253_v2_n3_p395_Chas |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
conjugacy classes embedded curves hyperbolic geometry intersection number Lie algebras Surfaces |
| spellingShingle |
conjugacy classes embedded curves hyperbolic geometry intersection number Lie algebras Surfaces Chas, M. Krongold, F. An algebraic characterization of simple closed curves on surfaces with boundary |
| topic_facet |
conjugacy classes embedded curves hyperbolic geometry intersection number Lie algebras Surfaces |
| description |
We prove that a conjugacy class in the fundamental group of a surface with boundary is represented by a power of a simple curve if and only if the Goldman bracket of two different powers of this class, one of them larger than two, is zero. The main theorem actually counts self-intersection number of a primitive class by counting the number of terms of the Goldman bracket of two distinct powers, one of them larger than two. © 2010 World Scientific Publishing Company. |
| format |
JOUR |
| author |
Chas, M. Krongold, F. |
| author_facet |
Chas, M. Krongold, F. |
| author_sort |
Chas, M. |
| title |
An algebraic characterization of simple closed curves on surfaces with boundary |
| title_short |
An algebraic characterization of simple closed curves on surfaces with boundary |
| title_full |
An algebraic characterization of simple closed curves on surfaces with boundary |
| title_fullStr |
An algebraic characterization of simple closed curves on surfaces with boundary |
| title_full_unstemmed |
An algebraic characterization of simple closed curves on surfaces with boundary |
| title_sort |
algebraic characterization of simple closed curves on surfaces with boundary |
| url |
http://hdl.handle.net/20.500.12110/paper_17935253_v2_n3_p395_Chas |
| work_keys_str_mv |
AT chasm analgebraiccharacterizationofsimpleclosedcurvesonsurfaceswithboundary AT krongoldf analgebraiccharacterizationofsimpleclosedcurvesonsurfaceswithboundary AT chasm algebraiccharacterizationofsimpleclosedcurvesonsurfaceswithboundary AT krongoldf algebraiccharacterizationofsimpleclosedcurvesonsurfaceswithboundary |
| _version_ |
1807317859316006912 |