Growth of quotients of groups acting by isometries on Gromov hyperbolic\n spaces

2012/12/29 by Stéphane Sabourau, Sabourau, Stephane
Mathematics · #20E07 #20F67 #20F69 #53C23 #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds #Group Theory (math.GR) #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1212.6611

openalex publication_date 2012/12/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that every non-elementary group G acting properly and cocompactly\nby isometries on a proper geodesic Gromov hyperbolic space X is growth tight.\nIn other words, the exponential growth rate of G for the geometric\n(pseudo)-distance induced by X is greater than the exponential growth rate of\nany of its quotients by an infinite normal subgroup. This result generalizes\nfrom a unified framework previous works of Arzhantseva-Lysenok and Sambusetti,\nand provides an answer to a question of the latter.\n

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