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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Detalles Bibliográficos
Autores principales:	Chas, Moira, Krongold, Fabiana
Publicado:	2010
Materias:	conjugacy classes embedded curves hyperbolic geometry intersection number Lie algebras Surfaces
Acceso en línea:	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_17935253_v2_n3_p395_Chas http://hdl.handle.net/20.500.12110/paper_17935253_v2_n3_p395_Chas
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

id	paper:paper_17935253_v2_n3_p395_Chas
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spelling	paper:paper_17935253_v2_n3_p395_Chas2023-06-08T16:29:07Z An algebraic characterization of simple closed curves on surfaces with boundary Chas, Moira Krongold, Fabiana 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. 2010 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_17935253_v2_n3_p395_Chas 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, Moira Krongold, Fabiana 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.
author	Chas, Moira Krongold, Fabiana
author_facet	Chas, Moira Krongold, Fabiana
author_sort	Chas, Moira
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
publishDate	2010
url	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_17935253_v2_n3_p395_Chas http://hdl.handle.net/20.500.12110/paper_17935253_v2_n3_p395_Chas
work_keys_str_mv	AT chasmoira analgebraiccharacterizationofsimpleclosedcurvesonsurfaceswithboundary AT krongoldfabiana analgebraiccharacterizationofsimpleclosedcurvesonsurfaceswithboundary AT chasmoira algebraiccharacterizationofsimpleclosedcurvesonsurfaceswithboundary AT krongoldfabiana algebraiccharacterizationofsimpleclosedcurvesonsurfaceswithboundary
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An algebraic characterization of simple closed curves on surfaces with boundary

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