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Volumes of hyperbolic Haken manifolds, I

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References

  1. M. Culler, P.B. Shalen: Paradoxical decompositions, 2-generator Kleinian groups and volumes of hyperbolic 3-manifolds. J. Am. Math. Soc.5 (1992) 231–288

    Google Scholar 

  2. M. Culler P.B. Shalen: Hyperbolic volume and modp homology. Preprint, University of Illinois at Chicago, 1992

  3. M. Culler, P.B. Shalen: The volume of a hyperbolic 3-manifold with Betti number 2. Preprint, University of Illinois at Chicago, 1992

  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. 189–230

    Google Scholar 

  5. F. Gehring, G. Martin: Inequalities for Möbius transformations and discrete group (Pre-print)

  6. J. Hempel: 3-manifolds. Ann. Math. Stud. vol. 86, Princeton University Press

  7. W. Jaco, P.B. Shalen: Peripheral structure of 3-manifolds. Memoirs Am. Math. Soc.21, 220 (1979)

    Google Scholar 

  8. K. Johannson: Homotopy equivalences of 3-manifolds with boundaries. Lecture Notes in Mathematics, vol. 761 Berlin Heidelberg: Springer 1979

    Google Scholar 

  9. R. Meyerhoff: Sphere-packing and volume in hyperbolic 3-space. Comm. Math. Helv.61 (1986) 271–278

    Google Scholar 

  10. R. Meyerhoff: A lower bound for the volume of hyperbolic 3-manifolds. Can. J. Math.34 (1987) 1038–1056

    Google Scholar 

  11. G.P. Scott: Subgroups of surface groups are almost geometric. J. London Math. Soc.17 (1978) 555–565

    Google Scholar 

  12. J.-P. Serre: Trees. New York: Springer 1980

    Google Scholar 

  13. P.B. Shalen, P. Wagreich: Growth rates,Z p -homology and volumes of hyperbolic 3-manifolds, Trans. Amer. Math. Soc.331 (1992) 895–917

    Google Scholar 

  14. J. Simon: Compactification of covering spaces of compact 3-manifolds. Michigan Math. J.23 (1976) 245–256

    Google Scholar 

  15. F. Waldhausen: On irreducible 3-manifolds which are sufficiently large. Ann. Math. (2)87 (1968) 56–88

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, University of Illinois at Chicago, 60680, Chicago, IL, USA

    Marc Culler & Peter B. Shalen

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  1. Marc Culler
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  2. Peter B. Shalen
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Oblatum 11-X-1993 & 20-XII-1993

Supported by an NSF grant

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Culler, M., Shalen, P.B. Volumes of hyperbolic Haken manifolds, I. Invent Math 118, 285–329 (1994). https://doi.org/10.1007/BF01231535

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