Growth of quotients of groups acting by isometries on Gromov-hyperbolic spaces | Zendy

Stéphane Sabourau | Zendy

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Growth of quotients of groups acting by isometries on Gromov-hyperbolic spaces

Author(s) -

Stéphane Sabourau

Publication year - 2013

Publication title -

journal of modern dynamics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.668

H-Index - 25

eISSN - 1930-532X

pISSN - 1930-5311

DOI - 10.3934/jmd.2013.7.269

Subject(s) - mathematics , quotient , pure mathematics , normal subgroup , exponential growth , hyperbolic space , growth rate , relatively hyperbolic group , hyperbolic manifold , group (periodic table) , combinatorics , discrete mathematics , mathematical analysis , hyperbolic function , geometry , chemistry , organic chemistry

International audienceWe show that every group G with no cyclic subgroup of finite index that acts properly and cocompactly by isometries on a proper geodesic Gromov hyperbolic space X is growth tight. In other words, the exponential growth rate of G for the geometric (pseudo)-distance induced by X is greater than the exponential growth rate of any of its quotients by an infinite normal subgroup. This result unifies and extends previous works of Arzhantseva-Lysenok and Sambusetti using a geometric approach

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