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...