Skip to main content
SpringerLink
Log in

Finite presentation of 3-manifold mapping class groups

  • Research Papers
  • Conference paper
  • First Online:
Groups of Self-Equivalences and Related Topics

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1425))

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 34.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 46.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. F. Bonahon, Cobordism of automorphisms of surfaces, Ann. École Norm. Sup. (4) 16 (1983), 237–270.

    MathSciNet  MATH  Google Scholar 

  2. F. Bonahon, Difféotopies des espaces lenticulaires, Topology 22 (1983), 305–314.

    Article  MathSciNet  MATH  Google Scholar 

  3. K. Brown, Presentations for groups acting on simply-connected complexes, J. Pure Appl. Alg. 32 (1984), 1–10.

    Article  MathSciNet  MATH  Google Scholar 

  4. J. Friedman and D. Witt, Homotopy is not isotopy for homeomorphisms of 3-manifolds, Topology 25 (1986), 35–44.

    Article  MathSciNet  MATH  Google Scholar 

  5. H. Gluck, The imbedding of two-spheres in four-spheres, Bull. Amer. Math. Soc. 67 (1961), 586–589.

    Article  MathSciNet  MATH  Google Scholar 

  6. D. Gottlieb, A certain subgroup of the fundamental group, Amer. J. Math. 87 (1965), 840–856.

    Article  MathSciNet  MATH  Google Scholar 

  7. P. Grasse, Finite presentation of mapping class groups of certain 3-manifolds, Topology Appl. 32 (1989), 205–305.

    Article  MathSciNet  MATH  Google Scholar 

  8. W. Heil, On ℙ2-irreducible 3-manifolds, Bull. Amer. Math. Soc. 75 (1969), 772–775.

    Article  MathSciNet  MATH  Google Scholar 

  9. H. Hendriks, Applications de la théorie d'obstruction en dimension 3, Bull. Soc. Math. France Mémoire 53 (1977), 81–196.

    MathSciNet  MATH  Google Scholar 

  10. H. Hendriks and F. Laudenbach, Difféomorphismes des sommes connexes en dimension trois, Topology 23 (1984), 423–443.

    Article  MathSciNet  MATH  Google Scholar 

  11. H. Hendriks and D. McCullough, On the diffeomorphism group of a reducible 3-manifold, Topology Appl. 26 (1987), 25–31.

    Article  MathSciNet  MATH  Google Scholar 

  12. W. Jaco and P. Shalen, Seifert fibered spaces in 3-manifolds, Mem. Amer. Math. Soc. 220 (1979), 1–192.

    MathSciNet  MATH  Google Scholar 

  13. K. Johannson, Homotopy equivalences of 3-manifolds with boundaries, Lecture Notes in Mathematics Vol. 761, Springer-Verlag, Berlin (1979).

    MATH  Google Scholar 

  14. J. Kalliongis and D. McCullough, π1-injective mappings of compact 3-manifolds, Proc. London Math. Soc. (3), 52 (1986), 173–192.

    Article  MathSciNet  MATH  Google Scholar 

  15. J. Kalliongis and D. McCullough, Maps inducing isomorphisms on fundamental groups of compact 3-manifolds, J. London Math. Soc. (2) 35 (1987), 177–192.

    Article  MathSciNet  MATH  Google Scholar 

  16. R. Kramer, The twist group of an orientable cube-with-two-handles is not finitely generated, preprint.

    Google Scholar 

  17. F. Laudenbach, Topologie de la dimension trois. Homotopie et isotopie, Astérisque 12 (1974), 1–152.

    MathSciNet  MATH  Google Scholar 

  18. G. S. McCarty, Homeotopy groups, Trans. Amer. Math. Soc. 106 (1963), 293–304.

    Article  MathSciNet  MATH  Google Scholar 

  19. D. McCullough, Virtual cohomological dimension of mapping class groups of 3-manifolds, Bull. Amer. Math. Soc. 18 (1988), 27–30.

    Article  MathSciNet  MATH  Google Scholar 

  20. D. McCullough, Virtually geometrically finite mapping class groups of 3-manifolds, to appear in J. Diff. Geom.

    Google Scholar 

  21. D. McCullough, Twist groups of compact 3-manifolds, Topology 24 (1985), 461–474.

    Article  MathSciNet  MATH  Google Scholar 

  22. D. McCullough, Mappings of reducible 3-manifolds, in Proceedings of the Semester in Geometric and Algebraic Topology of the Banach International Mathematical Center, ed. H. Torunczyk, Banach Center Publications, Warsaw (1986), 61–76.

    Google Scholar 

  23. D. McCullough, Homotopy groups of the space of self-homotopy-equivalences, Trans. Amer. Math. Soc. 264 (1981), 151–163.

    Article  MathSciNet  MATH  Google Scholar 

  24. D. McCullough, Automorphisms of punctured-surface bundles, in Geometry and Topology: Manifolds, Varieties, and Knots, ed. C. McCrory and T. Shifrin, Marcel-Dekker, New York (1987), 179–209.

    Google Scholar 

  25. G. Mess, Centers of 3-manifold groups and groups which are coarse quasiisometric to planes, preprint.

    Google Scholar 

  26. J. H. Rubinstein and J. Birman, One-sided Heegaard splittings and homeotopy groups of some 3-manifolds, Proc. London Math. Soc. (3) 49 (1984), 517–536.

    Article  MathSciNet  MATH  Google Scholar 

  27. P. Scott, Finitely generated 3-manifold groups are finitely presented, J. London Math. Soc. (2) 6 (1973), 437–440.

    Article  MathSciNet  MATH  Google Scholar 

  28. F. Waldhausen, On irreducible 3-manifolds which are sufficiently large, Annals of Math. 87 (1968), 56–88.

    Article  MathSciNet  MATH  Google Scholar 

  29. F. Waldhausen, Recent results on sufficiently large 3-manifolds, in Proceedings of Symposia in Pure Mathematics, Vol. 32, ed. R. J. Milgram (1978), 21–38.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Cornell University and the University of Oklahoma, USA

    Allen Hatcher & Darryl McCullough

Authors
  1. Allen Hatcher
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Darryl McCullough
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Renzo A. Piccinini

Rights and permissions

Reprints and permissions

Copyright information

© 1990 Springer-Verlag

About this paper

Cite this paper

Hatcher, A., McCullough, D. (1990). Finite presentation of 3-manifold mapping class groups. In: Piccinini, R.A. (eds) Groups of Self-Equivalences and Related Topics. Lecture Notes in Mathematics, vol 1425. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0083830

Download citation

  • DOI: https://doi.org/10.1007/BFb0083830

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-52658-2

  • Online ISBN: 978-3-540-47091-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation