Asymptotic cones and polynomial isoperimetric inequalities

Let Γ be a finitely presented group. We consider the relationship between the complexity of the word problem in Γ and the topology of asymptotic cones Cone ω Γ. We prove that there exist groups Γ which satisfy a polynomial isoperimetric inequality but do not have simply connected asymptotic cones. © 1999 Elsevier Science Ltd. All rights reserved.