Abstract
We give upper bounds for isoperimetric functions of semi-direct products
in terms of the asymptotic behaviour of ||A k|| ask → ∞. In the caseA ∈ 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 inNil andSol.
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Partially supported by NSF grant DMS-9203500.
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Bridson, M.R., Pittet, C. Isoperimetric inequalities for the fundamental groups of torus bundles over the circle. Geom Dedicata 49, 203–219 (1994). https://doi.org/10.1007/BF01610621
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DOI: https://doi.org/10.1007/BF01610621