On the dimension growth of groups

2010/08/23 by Dranishnikov, Alexander, Sapir, Mark
#Algebraic Topology (math.AT) #Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1008.3868

Abstract

Dimension growth functions of groups have been introduced by Gromov in 1999. We prove that every solvable finitely generated subgroups of the R. Thompson group F has polynomial dimension growth while the group F itself, and some solvable groups of class 3 have exponential dimension growth with exponential control. We describe connections between dimension growth, expansion properties of finite graphs and the Ramsey theory.

Related

• Groups with a polynomial dimension growth
• Growth of the asymptotic dimension function for groups
• A finitary version of Gromov's polynomial growth theorem
• Polynomially growing harmonic functions on connected groups
• Arbitrarily Large Residual Finiteness Growth