Isoperimetric inequalities for the fundamental groups of torus bundles over the circle

We give upper bounds for isoperimetric functions of semi-direct products[Figure not available: see fulltext.] in terms of the asymptotic behaviour of ||Ak|| as k → ∞. In the case A ∈ Sp(n, ℤ) we show that these bounds are sharp. This enables us to describe infinite families of nilpotent groups whose Dehn functions are bounded above and below by polynomials of degree the nilpotency class plus 1. We also recover the isoperimetric inequalities of cocompact lattices in Nil and Sol. © 1994 Kluwer Academic Publishers.