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Volume entropy for minimal presentations of surface groups in all ranks
Alsedà, Lluís (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Juher, David (Universitat de Girona. Departament d’Informàtica i Matemàtica Aplicada)
Los, Jérôme (Aix-Marseille Université. Institut Mathematiques de Marseille)
Mañosas, Francesc (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

 Data: 2015 Resum: We study the volume entropy of a class of presentations (including the classical ones) for all surface groups, called minimal geomètric presentations. We rediscover a formula first obtained by Cannon and Wagreich [6] with the computation in a non published manuscrit by Cannon [5]. 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 [3] and extended to all geometric presentations in [15]. 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 x n − 2(n − 1) nX−1 j=1 x j + 1. Nota: Número d'acord de subvenció MINECO/MTM2008-01486 Nota: Número d'acord de subvenció MINECO/MTM2011-26995-C02-01 Nota: Agraïments: This work has been carried out thanks to the support of the ARCHIMEDE Labex (ANR-11-LABX- 0033). Drets: Tots els drets reservats. Llengua: Anglès. Document: article ; recerca ; submittedVersion Matèria: Bowen-Series Markov maps ; Surface groups ; Topological entropy ; Volume entropy Publicat a: Geometriae Dedicata, 2015 , ISSN 1572-9168

DOI: 10.1007/s10711-015-0103-7

 Preprint 31 p, 536.4 KB

Registre creat el 2016-01-12, darrera modificació el 2018-11-06

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