Finitely presented groups with infinitely many non-homeomorphic asymptotic cones

2011/08/10 by Osin, Denis, Houcine, Abderezak Ould
#20B07 #20F65 #20F69 #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1108.2100

Abstract

We construct a finitely presented group with infinitely many non-homeomorphic asymptotic cones. We also show that the existence of cut points in asymptotic cones of finitely presented groups does, in general, depend on the choice of scaling constants and ultrafilters.

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