The optimal isoperimetric inequality for torus bundles over the circle

Quarterly Journal of Mathematics

Volumn 47, Issue 185, 1996, Pages 1-23

  Bridson, M R ^a,b   Gersten, S M ^c  

^a PRINCETON UNIVERSITY   (United States)

^b UNIVERSITY OF OXFORD   (United Kingdom)

^c UNIVERSITY OF UTAH   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030304659     PISSN: 00335606     EISSN: None     Source Type: Journal    
DOI: 10.1093/qjmath/47.185.1     Document Type: Article

References (32)

1. J. M. Alonso, 'Inégalités isopérimétriques et quasi-isométries', C.R.A.S. Paris Série 1 311 (1990), 761-764.
2. J. M. Alonso and M. R. Bridson, 'Semihyperbolic groups', Proc. London Math. Soc. (3) 70 (1995), 56-114.
3. 2 par ℤ', Rapport de Recherche No. 31, E.N.S. Lyon (1990).
4. H. Bass, 'The degree of polynomial growth of finitely generated nilpotent groups', Proc. London Math. Soc. (3) 25 (1972), 603-614.
5. G. Baumslag, C. F. Miller III, and H. Short, 'Isoperimetric inequalities and the homology of groups', Invent. Math. 113 (1993), 531-500.
6. M. R. Bridson, 'Combings of semidirect products and 3-manifold groups', Geom. and Funct. Anal. (GAFA) 3 (1993), 263-278.
7. M. R. Bridson, 'On the geometry of normal forms in discrete groups', Proc. London Math. Soc. (3) 67 (1993), 596-616.
8. M. R. Bridson, 'Optimal isoperimetric inequalities for abelian-by-free groups', Topology 34 (1995), 547-564.
9. M. R. Bridson and Ch. Pittet, 'Isoperimetric inequalities for the fundamental groups of torus bundles over the circle', Geom. Dedicata 27 (1994), 203-219.
10. K. S. Brown, 'Cohomology of Groups', Graduate texts in Mathematics, vol. 87, Springer-Verlag, 1982.
11. A. Casson and S. Bleiler, 'Automorphisms of surfaces after Nielsen and Thurston', Cambridge Univ. Press, 1988.
12. D. B. A. Epstein, J. W. Cannon, D. F. Holt, S. V. F. Levy, M. S. Paterson, and W. P. Thurston, 'Word processing in groups', Bartlett and Jones, Boston, 1992.
13. 1-norms of finite presentations', Algorithmic problems and classification in group theory (G. Baumslag and C. F. Miller III, eds.), MSRI Series, vol. 23, Springer-Verlag, 1992.
14. S. M. Gersten, 'Isoperimetric and isodiametric functions of finite presentations', Geometric Group Theory Volume 1 (G. Niblo and M. Roller, eds.), London Math. Soc. Lecture Notes Series, vol. 181, Cambridge Univ. Press, 1993, pp. 79-96.
15. S. M. Gersten, 'Isoperimetric and isodiametric functions of finite presentations', Geometric Group Theory Volume 1 (G. Niblo and M. Roller, eds.), London Math. Soc. Lecture Notes Series, vol. 181, Cambridge Univ. Press, 1993, pp. 79-96.
16. S. M. Gersten, 'Bounded cohomology and combings of groups', preprint, Univ. of Utah 1992.
17. S. M. Gersten, 'Quasi-isometry invariance of cohomological dimension', Comptes Rendus Acad. Sci. Paris Série 1 Math. 316 (1993), 411-416.
18. E. Ghys and P. de la Harpe, editors, 'Sur les groupes hyperboliques d'aprés Mikhael Gromov', Birkhäuser, 1990.
19. E. Ghys, 'Les groupes hyperboliques', Séminaire Bourbaki no. 722, Astérisque 189-190 (1990).
20. M. Gromov, 'Hyperbolic groups', Essays in group theory (S. M. Gersten, ed.), MSRI series vol. 8, Springer-Verlag, 1987.
21. M. Gromov, 'Asymptotic invariants of infinite groups', Geometric Group Theory Volume 2 ( G. Niblo and M. Roller, eds.), London Math. Soc. Lecture Notes Series, vol. 182, Cambridge Univ. Press, 1993.
22. M. Gromov, 'Asymptotic invariants of infinite groups', Geometric Group Theory Volume 2 ( G. Niblo and M. Roller, eds.), London Math. Soc. Lecture Notes Series, vol. 182, Cambridge Univ. Press, 1993.
23. M. Gromov, 'Groups of polynomial growth and expanding maps', IHES Publ. Math. Sci. 53 (1981), 53-78.
24. S. M. Gersten and H. B. Short, 'Rational subgroups of biautomatic groups', Annals of Math. 134 (1990), 125-158.
25. D. Gromoll and J. Wolf, 'Some relations between the metric structure and the algebraic structure of the fundamental group in manifolds of non-positive curvature', Bull. A. M.S. 77 (1971), 545-552.
26. R. C. Lyndon and P. E. Schupp, 'Combinatorial group theory', Springer-Verlag, 1977.
27. H. B. Lawson and S. T. Yau, 'Compact manifolds of nonpositive curvature', Jour. Diff. Geom. 7 (1972), 211-228.
28. P. Pansu, "Métriques de Carnot-Carathéodory et quasiisométries des espaces symétriques de rang un', Annals. of Math. 129 (1989), 1-60.
29. M. S. Raghunathan, 'Discrete subgroups of Lie groups', Springer-Verlag, 1972.
30. G. P. Scott, 'The geometries of 3-manifolds', Bull. London Math. Soc. 15 (1983), 401-487.
31. D. Segal, 'Polycyclic Groups', Cambridge Univ. Press, 1983.
32. C. L. Siegel, 'Algebraic integers whose conjugates lie in the unit circle', Duke Math. Jour. 11 (1944), 597-602.