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AlsedÃ , LluÃs
Juher, David Los, JÃ©rÃ´me MaÃ±osas, Francesc 

2016  
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), 239â€“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 Ã‰tudes Sci Publ Math 50, 153â€“170, 1979) and extended to all geometric presentations in Los (J Topol, 7(1), 120â€“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(Î»n), where Î»n is the unique real root larger than one of the polynomial  
application/pdf  
024213  
00465755 (versiÃ³ paper) 15729168 (versiÃ³ electrÃ²nica) 

http://hdl.handle.net/10256/11992  
eng  
Springer Verlag  
VersiÃ³ postprint del document publicat a: http://dx.doi.org/10.1007/s1071101501037 Articles publicats (DIMAE) 

Â© Geometriae Dedicata, 2016, vol. 180, nÃºm. 1, p. 292322  
Tots els drets reservats  
Entropia topolÃ²gica
Topological entropy 

Volume entropy for minimal presentations of surface groups in all ranks  
info:eurepo/semantics/article  
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