Skip to main content

Coxeter groups and aspherical manifolds

  • Geometry Of Manifolds
  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1051))

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   54.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   69.95
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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. E. M. Andreev, On convex polyhedra in Lobacevskii spaces, Math. USSR Sbornik 10(1970) No. 5, 413–440.

    Article  Google Scholar 

  2. N. Bourbaki, Groupes et Algebres de Lie, Chapters IV–VI, Hermann, Paris 1968.

    MATH  Google Scholar 

  3. M. Davis, Groups generated by reflections and aspherical manifolds not covered by Euclidean space, to appear in Ann. of Math. 117(1983).

    Google Scholar 

  4. F. T. Farrell and W. C. Hsiang, On Novikov's conjecture for non-positively curved manifolds, I. Ann. of Math. 113(1981), 199–209.

    Article  MathSciNet  MATH  Google Scholar 

  5. M. Freedman, The topology of four-dimensional manifolds, J. Diff. Geom. 17(1982), 357–453.

    MathSciNet  MATH  Google Scholar 

  6. B. Jackson, End invariants of group extensions, Topology 21(1981), 71–81.

    Article  MathSciNet  MATH  Google Scholar 

  7. F. E. A. Johnson, Manifolds of homotopy type K(π,l). II, Proc. Cambridge Phil. Soc. 75(1974), 165–173.

    Article  MathSciNet  Google Scholar 

  8. M. Kato, Some problems in topology. Manifolds-Tokyo 1973 (pp. 421–431), University of Tokyo Press, Tokyo 1975.

    Google Scholar 

  9. M. A. Kervaire, Smooth homology spheres and their fundamental groups. Amer. Math. Soc. Trans. 144(1969), 67–72.

    Article  MathSciNet  MATH  Google Scholar 

  10. R. Lee and F. Raymond, Manifolds covered by Euclidean space, Topology 14(1975), 49–57.

    Article  MathSciNet  MATH  Google Scholar 

  11. B. Mazur, A note on some contractible 4-manifolds, Ann. of Math. (2) 73(1961), 221–228.

    Article  MathSciNet  MATH  Google Scholar 

  12. M. H. A. Newman, Boundaries of ULC sets in Euclidean n-space. Proc. N.A.S. 34(1948), 193–196.

    Article  MathSciNet  MATH  Google Scholar 

  13. _____, The engulfing theorem for topological manifolds, Ann. of Math. 84(1966), 555–571.

    Article  MathSciNet  MATH  Google Scholar 

  14. V. Poénaru, Les decompositions de l'hypercube en produit topologique, Bull. Soc. Math. France 88(1960), 113–129.

    MathSciNet  MATH  Google Scholar 

  15. A. Selberg, On discontinuous groups in higher dimensional symmetric spaces, Int. Colloquim on Function Theory, Tata Institute, Bombay, 1960.

    Google Scholar 

  16. J. P. Serre, Cohomologie des groupes discrets, Prospects in Mathematics, Ann. Math. Studies Vol. 70 (pp. 77–169), Princeton University Press, Princeton 1971.

    Google Scholar 

  17. L. C. Siebenmann, The obstruction to finding a boundary for an open manifold of dimension ≥ 5, thesis, Princeton 1965.

    Google Scholar 

  18. S. Smale, Generalized Poincare's conjecture in dimensions greater than four, Ann. of Math. (2) 74(1961), 391–406.

    Article  MathSciNet  MATH  Google Scholar 

  19. J. Stallings, Polyhedral homotopy-spheres, Bull. Amer. Math. Soc. 66(1960), 485–488.

    Article  MathSciNet  MATH  Google Scholar 

  20. _____, The piecewise-linear structure of euclidean space, Proc. Cambridge Phil. Soc. 58(1962), 481–488.

    Article  MathSciNet  MATH  Google Scholar 

  21. W. Thurston, The Geometry and Topology of 3-Manifolds, Chapter 5: "Orbifolds," to appear in Princeton Math. Series, Princeton University Press, Princeton 1983.

    Google Scholar 

  22. J. H. C. Whitehead, A certain open manifold whose group is unity (pp. 39–50), On the group of a certain linkage (with M. H. A. Newman) (pp. 51–58). The Mathematical Works of J.H.C. Whitehead, Vol. II Mac Millan, New York 1963.

    Google Scholar 

Download references

Authors

Editor information

Ib H. Madsen Robert A. Oliver

Rights and permissions

Reprints and permissions

Copyright information

© 1984 Springer-Verlag

About this paper

Cite this paper

Davis, M.W. (1984). Coxeter groups and aspherical manifolds. In: Madsen, I.H., Oliver, R.A. (eds) Algebraic Topology Aarhus 1982. Lecture Notes in Mathematics, vol 1051. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0075568

Download citation

  • DOI: https://doi.org/10.1007/BFb0075568

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-12902-8

  • Online ISBN: 978-3-540-38782-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics