Submission date: 11 August 2011.

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.

Mathematics Subject Classification: 20B07, 20F69, 20F65

Keywords and phrases: finitely presented groups, asymptotic cones, non-homeomorphic

Full text arXiv 1108.2100: pdf, ps.