Finitely presented simple groups with at least exponential Dehn function

Abstract

We construct examples of finitely presented simple groups whose Dehn functions are at least exponential. To the best of our knowledge, these are the first such examples known. Our examples arise from Röver-Nekrashevych groups, using carefully calibrated self-similar representations of Baumslag-Solitar groups.

arXiv comment11 pages. v2: Following referee report, made minor changes and fixed a computational error in the proof of Prop 3.1. Final version, to appear in Michigan Math. J