Skip to main content

Some theorems on topological manifolds

Geometric Topology

Part of the Lecture Notes in Mathematics book series (LNM,volume 197)

Keywords

  • Manifold Structure
  • Topological Manifold
  • Classification Theorem
  • Whitehead Torsion
  • Simple HomotopY Type

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   34.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   46.00
Price excludes VAT (Canada)
  • 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. Cooke, G., Hauptvermutung according to Sullivan, Lecture notes, Inst. for Advanced Study, 1968.

    Google Scholar 

  2. Haefliger, A., and Poenaru, V., La Classification des Immersion Combinatoires, Publ. Math. Inst. Hautes Etudes Sci., 23(1964), 75–91.

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. Hirsch, M., On Combinatorial Submanifolds of Differentiable Manifolds, Comment. Math. Helv., 36(1962), 103–111.

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. Hirsch, M., Smoothings of Piecewise-Linear Manifolds I: Products, Preprint Geneva and Berkeley, 1969.

    Google Scholar 

  5. Kirby, R., Stable Homeomorphisms and the Annulus Conjecture, Ann. of Math., 89(1969), 575–582.

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. Kirby, R., Lectures on Triangulations of Manifolds, Lecture notes, UCLA, 1969.

    Google Scholar 

  7. Kirby, R., and Siebenmann, L., On the Triangulation of Manifolds and the Hauptvermutung, Bull. Amer. Math. Soc., 75(1969), 742–749.

    CrossRef  MathSciNet  MATH  Google Scholar 

  8. Kirby, R., and Siebenmann, L., Notices Amer. Math. Soc., 16(1969), 848,695,698.

    Google Scholar 

  9. Kirby, R., and Siebenmann, L., Deformation of Smooth and Piecewise Linear Manifold Structures, to appear.

    Google Scholar 

  10. Kirby, R., and Siebenmann, L., Classification of Smooth and Piecewise-Linear Manifold Structures, to appear.

    Google Scholar 

  11. Kirby, R., and Siebenmann, L., to appear.

    Google Scholar 

  12. Lashof, R., The Immersion Approach to Triangulations, Proc. Athens, Georgia Topology Conference, August 1969.

    Google Scholar 

  13. Lashof, R., and Rothenberg, M., Triangulation of Manifolds. I, II., Bull. Amer. Math. Soc., 75(1969), 750–757.

    CrossRef  MathSciNet  MATH  Google Scholar 

  14. Milnor, J., Microbundles, I. Topology, 3 Supplement 1(1964), 53–80.

    CrossRef  MathSciNet  MATH  Google Scholar 

  15. Morlet, C., Hauptvermutung et Triangulation des Variétés, Sém. Bourbaki (1968–69), Exposé 362.

    Google Scholar 

  16. Munkres, J., Concordance is Equivalent to Smoothability, Topology 5(1966), 371–389.

    CrossRef  MathSciNet  MATH  Google Scholar 

  17. Rourke, C., Hauptvermutung According to Sullivan, I, II, Lecture notes, Inst. Advanced Study, 1968.

    Google Scholar 

  18. Siebenmann, L., A Total Whitehead Torsion Obstruction, Comment. Math. Helv., 45(1970), 1–48.

    CrossRef  MathSciNet  MATH  Google Scholar 

  19. Siebenmann, L., Infinite Simple Homotopy Types, Indag. Math., 32 (1970), 479–495.

    CrossRef  MathSciNet  MATH  Google Scholar 

  20. Siebenmann, L., Disruption of low dimensional handlebody theory by Rohlin's theorem, Proc. Athens, Georgia Topology Conference, August 1969.

    Google Scholar 

  21. Sullivan, D., On the Hauptvermutung for Manifolds, Bull. Amer. Math. Soc., 73(1967), 598–600.

    CrossRef  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1971 Springer-Verlag

About this paper

Cite this paper

Kirby, R.C., Siebenmann, L.C. (1971). Some theorems on topological manifolds. In: Kuiper, N.H. (eds) Manifolds — Amsterdam 1970. Lecture Notes in Mathematics, vol 197. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0068607

Download citation

  • DOI: https://doi.org/10.1007/BFb0068607

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-05467-2

  • Online ISBN: 978-3-540-36653-9

  • eBook Packages: Springer Book Archive