THE GEOMETRY OF ONE-RELATOR GROUPS SATISFYING A POLYNOMIAL ISOPERIMETRIC INEQUALITY

摘要

For every pair of positive integers p q we construct a one-relator group R-p,R-q whose Dehn function is similar or equal to n(2 alpha) where alpha = log(2)(2p/q). The group R-p,R-q has no subgroup isomorphic to a Baumslag-Solitar group BS(m, n) with m not equal +/- n, but it 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.