Skip to main content

Generalized three-manifolds

  • Conference paper
  • First Online:
Shape Theory and Geometric Topology

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 870))

  • 377 Accesses

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

Access this chapter

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 69.99
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. R.H. Bing, A homeomorphism between the 3-sphere and the sum of two Alexander horned spheres, Ann. of Maths. (2) 56 (1952), 354–362.

    Article  MathSciNet  MATH  Google Scholar 

  2. _____, Decompositions of E3, Topology of 3-Manifolds (M.K. Fort, ed.), Prentice-Hall, Englewood Cliffs, N.J., 1962, pp. 5–20.

    Google Scholar 

  3. G.E. Bredon, Wilder manifolds are locally orientable, Proc. Nat. Acad. Sci. U.S.A. 63 (1969), 1079–1081.

    Article  MathSciNet  MATH  Google Scholar 

  4. M. Brin, Generalized 3-manifolds whose non-manifold set has neighborhoods bounded by tori, Trans. Amer. Math. Soc. (forthcoming).

    Google Scholar 

  5. M. Brin and D.R. McMillan, Jr., Generalized three-manifolds with zero-dimensional non-manifold set (to appear).

    Google Scholar 

  6. M. Brown, A proof of the generalized Schoenflies theorem, Bull. Amer. Math. Soc., 66 (1960), 74–76.

    Article  MathSciNet  MATH  Google Scholar 

  7. J.L. Bryant and R.C. Lacher, Resolving acyclic images of three-manifolds, Math. Proc. Camb. Phil. Soc. 88 (1980), 311–319.

    Article  MathSciNet  MATH  Google Scholar 

  8. J.W. Cannon, Shrinking cell-like decompositions of manifolds: co-dimension three, Ann. of Math. (2) 110 (1979), 83–112.

    Article  MathSciNet  MATH  Google Scholar 

  9. _____, The characterization of topological manifolds of dimension n ≥ 5, Proc. Int. Cong. Math. (Helsinki, 1978), Academia Scientiarum Fennica, 1980.

    Google Scholar 

  10. R.J. Daverman, Decomposition Spaces (lectures given in Austin, Texas, Summer 1980) (to appear).

    Google Scholar 

  11. R.J. Daverman and J.J. Walsh, A ghastly generalized n-manifold (to appear).

    Google Scholar 

  12. C.H. Edwards, Jr., Open 3-manifolds which are simply connected at infinity, Proc. Amer. Math. Soc. 14 (1963), 391–395.

    MathSciNet  MATH  Google Scholar 

  13. R.D. Edwards, The topology of manifolds and cell-like maps. Proc. Int. Cong. Math. (Helsinki, 1978), Academia Scientiarum Fennica, 1980.

    Google Scholar 

  14. D.E. Galewski, J.G. Hollingsworth, and D.R. McMillan, Jr., On the fundamental group and homotopy type of open 3-manifolds, General Topology and Appl. 2 (1972), 299–313.

    Article  MathSciNet  MATH  Google Scholar 

  15. G. Kozlowski and J.J. Walsh, The cell-like mapping problem, Bull. Amer. Math. Soc. (2) 2 (1980), 315–316.

    Article  MathSciNet  MATH  Google Scholar 

  16. T. Knoblauch, Imbedding deleted 3-manifold neighborhoods in E3. Illinois J. Math. 18 (1974), 598–601.

    MathSciNet  MATH  Google Scholar 

  17. _____, Imbedding compact 3-manifolds in E3, Proc. Amer. Math. Soc. 48 (1975), 447–453.

    MathSciNet  MATH  Google Scholar 

  18. R.C. Lacher, Cell-like mappings and their generalizations, Bull. Amer. Math. Soc. 83 (1977), 495–552.

    Article  MathSciNet  MATH  Google Scholar 

  19. R.C. Lacher, Resolutions of generalized manifolds, Proc. Steklov Maths. Inst. 154 (forthcoming).

    Google Scholar 

  20. D.R. McMillan, Jr., Strong homotopy equivalence of 3-manifolds, Bull. Amer. Math. Soc. 73 (1967), 718–722.

    Article  MathSciNet  MATH  Google Scholar 

  21. __________, Acyclicity in 3-manifolds, Bull. Amer. Math. Soc. 76 (1970), 942–964.

    Article  MathSciNet  MATH  Google Scholar 

  22. __________, Heegaard splittings of homology 3-spheres and homotopy 3-spheres (to appear).

    Google Scholar 

  23. D.R. McMillan, Jr., and T.L. Thickstun, Open three-manifolds and the Poincaré conjecture, Topology 19 (1980), 313–320.

    Article  MathSciNet  MATH  Google Scholar 

  24. F. Quinn, Ends of maps, I, Ann. of Math. (2) 110 (1979), 275–331.

    Article  MathSciNet  MATH  Google Scholar 

  25. T.L. Thickstun, Open acyclic 3-manifolds, a loop theorem, and the Poincaré conjecture (to appear).

    Google Scholar 

  26. J.H.C. Whitehead, A certain open manifold whose group is unity, Quart. J. Maths. (Oxford series) 6 (1935), 268–279.

    Article  MATH  Google Scholar 

  27. R.L. Wilder, Generalized Manifolds, Amer. Math. Soc. Colloq. Publ. 32 (American Mathematical Society, Providence, R.I., 1949).

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Sibe Mardešić Jack Segal

Rights and permissions

Reprints and permissions

Copyright information

© 1981 Springer-Verlag

About this paper

Cite this paper

Lacher, R.C. (1981). Generalized three-manifolds. In: Mardešić, S., Segal, J. (eds) Shape Theory and Geometric Topology. Lecture Notes in Mathematics, vol 870. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0089709

Download citation

  • DOI: https://doi.org/10.1007/BFb0089709

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-10846-7

  • Online ISBN: 978-3-540-38749-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics