Geometriae Dedicata

, Volume 49, Issue 2, pp 203–219

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

  • M. R. Bridson
  • Ch. Pittet

DOI: 10.1007/BF01610621

Cite this article as:
Bridson, M.R. & Pittet, C. Geom Dedicata (1994) 49: 203. doi:10.1007/BF01610621


We give upper bounds for isoperimetric functions of semi-direct products
in terms of the asymptotic behaviour of ||Ak|| 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.

Copyright information

© Kluwer Academic Publishers 1994

Authors and Affiliations

  • M. R. Bridson
    • 1
  • Ch. Pittet
    • 2
  1. 1.Department of Mathematics, Fine HallPrinceton UniversityPrincetonUSA
  2. 2.Section de MathématiquesUniversité de GenèveGenève 24Switzerland