Volume entropy for minimal presentations of surface groups in all ranks

We study the volume entropy of a class of presentations (including the classical ones) for all surface groups, called minimal geometric presentations. We rediscover a formula first obtained by Cannon and Wagreich (Math Ann 293(2), 239–257, 1992) with the computation in a non published manuscript by...

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Autores: Alsedà i Soler, Lluís, Juher, David, Los, Jérôme, Mañosas, Francesc
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2016
País:España
Institución:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Repositorio:Recercat. Dipósit de la Recerca de Catalunya
OAI Identifier:oai:recercat.cat:10256/11992
Acceso en línea:http://hdl.handle.net/10256/11992
Access Level:acceso abierto
Palabra clave:Entropia topològica
Topological entropy
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spelling Volume entropy for minimal presentations of surface groups in all ranksAlsedà i Soler, LluísJuher, DavidLos, JérômeMañosas, FrancescEntropia topològicaTopological entropyWe study the volume entropy of a class of presentations (including the classical ones) for all surface groups, called minimal geometric presentations. We rediscover a formula first obtained by Cannon and Wagreich (Math Ann 293(2), 239–257, 1992) with the computation in a non published manuscript by Cannon (The growth of the closed surface groups and the compact hyperbolic coxeter groups, 1980). The result is surprising: an explicit polynomial of degree n, the rank of the group, encodes the volume entropy of all classical presentations of surface groups. The approach we use is completely different. It is based on a dynamical system construction following an idea due to Bowen and Series (Inst Hautes Études Sci Publ Math 50, 153–170, 1979) and extended to all geometric presentations in Los (J Topol, 7(1), 120–154, 2013). The result is an explicit formula for the volume entropy of minimal presentations for all surface groups, showing a polynomial dependence in the rank n>2. We prove that for a surface group Gn of rank n with a classical presentation Pn the volume entropy is log(λn), where λn is the unique real root larger than one of the polynomialSpringer Verlag2016info:eu-repo/semantics/articleinfo:eu-repo/semantics/acceptedVersion31 p.application/pdfhttp://hdl.handle.net/10256/11992http://hdl.handle.net/10256/11992© Geometriae Dedicata, 2016, vol. 180, núm. 1, p. 292-322Articles publicats (D-IMAE)Alsedà, Lluís Juher, David Los, Jérôme Mañosas, Francesc 2016 Volume entropy for minimal presentations of surface groups in all ranks Geometriae Dedicata 180 1 292 322reponame:Recercat. Dipósit de la Recerca de Catalunyainstname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)Inglésinfo:eu-repo/semantics/altIdentifier/doi/10.1007/s10711-015-0103-7info:eu-repo/semantics/altIdentifier/issn/0046-5755info:eu-repo/semantics/altIdentifier/eissn/1572-9168Tots els drets reservatsinfo:eu-repo/semantics/openAccessoai:recercat.cat:10256/119922026-05-29T05:05:01Z
dc.title.none.fl_str_mv Volume entropy for minimal presentations of surface groups in all ranks
title Volume entropy for minimal presentations of surface groups in all ranks
spellingShingle Volume entropy for minimal presentations of surface groups in all ranks
Alsedà i Soler, Lluís
Entropia topològica
Topological entropy
title_short Volume entropy for minimal presentations of surface groups in all ranks
title_full Volume entropy for minimal presentations of surface groups in all ranks
title_fullStr Volume entropy for minimal presentations of surface groups in all ranks
title_full_unstemmed Volume entropy for minimal presentations of surface groups in all ranks
title_sort Volume entropy for minimal presentations of surface groups in all ranks
dc.creator.none.fl_str_mv Alsedà i Soler, Lluís
Juher, David
Los, Jérôme
Mañosas, Francesc
author Alsedà i Soler, Lluís
author_facet Alsedà i Soler, Lluís
Juher, David
Los, Jérôme
Mañosas, Francesc
author_role author
author2 Juher, David
Los, Jérôme
Mañosas, Francesc
author2_role author
author
author
dc.subject.none.fl_str_mv Entropia topològica
Topological entropy
topic Entropia topològica
Topological entropy
description We study the volume entropy of a class of presentations (including the classical ones) for all surface groups, called minimal geometric presentations. We rediscover a formula first obtained by Cannon and Wagreich (Math Ann 293(2), 239–257, 1992) with the computation in a non published manuscript by Cannon (The growth of the closed surface groups and the compact hyperbolic coxeter groups, 1980). The result is surprising: an explicit polynomial of degree n, the rank of the group, encodes the volume entropy of all classical presentations of surface groups. The approach we use is completely different. It is based on a dynamical system construction following an idea due to Bowen and Series (Inst Hautes Études Sci Publ Math 50, 153–170, 1979) and extended to all geometric presentations in Los (J Topol, 7(1), 120–154, 2013). The result is an explicit formula for the volume entropy of minimal presentations for all surface groups, showing a polynomial dependence in the rank n>2. We prove that for a surface group Gn of rank n with a classical presentation Pn the volume entropy is log(λn), where λn is the unique real root larger than one of the polynomial
publishDate 2016
dc.date.none.fl_str_mv 2016
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/acceptedVersion
format article
status_str acceptedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/10256/11992
http://hdl.handle.net/10256/11992
url http://hdl.handle.net/10256/11992
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1007/s10711-015-0103-7
info:eu-repo/semantics/altIdentifier/issn/0046-5755
info:eu-repo/semantics/altIdentifier/eissn/1572-9168
dc.rights.none.fl_str_mv Tots els drets reservats
info:eu-repo/semantics/openAccess
rights_invalid_str_mv Tots els drets reservats
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 31 p.
application/pdf
dc.publisher.none.fl_str_mv Springer Verlag
publisher.none.fl_str_mv Springer Verlag
dc.source.none.fl_str_mv © Geometriae Dedicata, 2016, vol. 180, núm. 1, p. 292-322
Articles publicats (D-IMAE)
Alsedà, Lluís Juher, David Los, Jérôme Mañosas, Francesc 2016 Volume entropy for minimal presentations of surface groups in all ranks Geometriae Dedicata 180 1 292 322
reponame:Recercat. Dipósit de la Recerca de Catalunya
instname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
instname_str Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
reponame_str Recercat. Dipósit de la Recerca de Catalunya
collection Recercat. Dipósit de la Recerca de Catalunya
repository.name.fl_str_mv
repository.mail.fl_str_mv
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