Inventiones mathematicae

, Volume 118, Issue 1, pp 285–329 | Cite as

Volumes of hyperbolic Haken manifolds, I

  • Marc Culler
  • Peter B. Shalen


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  1. 1.
    M. Culler, P.B. Shalen: Paradoxical decompositions, 2-generator Kleinian groups and volumes of hyperbolic 3-manifolds. J. Am. Math. Soc.5 (1992) 231–288Google Scholar
  2. 2.
    M. Culler P.B. Shalen: Hyperbolic volume and modp homology. Preprint, University of Illinois at Chicago, 1992Google Scholar
  3. 3.
    M. Culler, P.B. Shalen: The volume of a hyperbolic 3-manifold with Betti number 2. Preprint, University of Illinois at Chicago, 1992Google Scholar
  4. 4.
    M. Culler, K. Vogtmann: The boundary of outer space in rank two. in: Arboreal group theory: Proceedings of a workshop held September 13–16, 1988, Roger C. Alperin, ed. MSRI Publ. 19, Berlin Heidelberg New York: Springer, 1991, pp. 189–230Google Scholar
  5. 5.
    F. Gehring, G. Martin: Inequalities for Möbius transformations and discrete group (Pre-print)Google Scholar
  6. 6.
    J. Hempel: 3-manifolds. Ann. Math. Stud. vol. 86, Princeton University PressGoogle Scholar
  7. 7.
    W. Jaco, P.B. Shalen: Peripheral structure of 3-manifolds. Memoirs Am. Math. Soc.21, 220 (1979)Google Scholar
  8. 9.
    K. Johannson: Homotopy equivalences of 3-manifolds with boundaries. Lecture Notes in Mathematics, vol. 761 Berlin Heidelberg: Springer 1979Google Scholar
  9. 10.
    R. Meyerhoff: Sphere-packing and volume in hyperbolic 3-space. Comm. Math. Helv.61 (1986) 271–278Google Scholar
  10. 11.
    R. Meyerhoff: A lower bound for the volume of hyperbolic 3-manifolds. Can. J. Math.34 (1987) 1038–1056Google Scholar
  11. 12.
    G.P. Scott: Subgroups of surface groups are almost geometric. J. London Math. Soc.17 (1978) 555–565Google Scholar
  12. 13.
    J.-P. Serre: Trees. New York: Springer 1980Google Scholar
  13. 14.
    P.B. Shalen, P. Wagreich: Growth rates,Z p-homology and volumes of hyperbolic 3-manifolds, Trans. Amer. Math. Soc.331 (1992) 895–917Google Scholar
  14. 15.
    J. Simon: Compactification of covering spaces of compact 3-manifolds. Michigan Math. J.23 (1976) 245–256Google Scholar
  15. 16.
    F. Waldhausen: On irreducible 3-manifolds which are sufficiently large. Ann. Math. (2)87 (1968) 56–88Google Scholar

Copyright information

© Springer-Verlag 1994

Authors and Affiliations

  • Marc Culler
    • 1
  • Peter B. Shalen
    • 1
  1. 1.Department of MathematicsUniversity of Illinois at ChicagoChicagoUSA

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