The geometry of one-relator groups satisfying a polynomial isoperimetric inequality

Abstract

For every pair of positive integers $p>q$ we construct a one-relator group $R_{p,q}$ whose Dehn function is $\simeq n^{2\alpha }$ where $\alpha ={\log }_2(2p/q)$. The group $R_{p,q}$ has no subgroup isomorphic to a Baumslag-Solitar group $BS(m,n)$ with $m\ne \pm n$, but is not automatic, not CAT(0), and cannot act freely on a CAT(0) cube complex. This answers a long-standing question on the automaticity of one-relator groups and gives counterexamples to a conjecture of Wise.

6 pages, 1 figure; v3 final version to appear in Proceedings of the American Mathematical Society; v2 correct remark about residual finiteness

Cited by in corpus (1)

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