Volume entropy for minimal presentations of surface groups in all ranks
dc.contributor.author
dc.date.accessioned
2016-01-29T11:06:12Z
dc.date.available
2017-02-02T04:00:05Z
dc.date.issued
2016
dc.identifier.issn
0046-5755
dc.identifier.uri
dc.description.abstract
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
dc.format.extent
31 p.
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application/pdf
dc.language.iso
eng
dc.publisher
Springer Verlag
dc.relation.isformatof
Versió postprint del document publicat a: http://dx.doi.org/10.1007/s10711-015-0103-7
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© Geometriae Dedicata, 2016, vol. 180, núm. 1, p. 292-322
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Articles publicats (D-IMAE)
dc.rights
Tots els drets reservats
dc.source
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
dc.subject
dc.title
Volume entropy for minimal presentations of surface groups in all ranks
dc.type
info:eu-repo/semantics/article
dc.rights.accessRights
info:eu-repo/semantics/openAccess
dc.type.version
info:eu-repo/semantics/acceptedVersion
dc.identifier.doi
dc.identifier.idgrec
024213
dc.identifier.eissn
1572-9168