Skip to main content
SpringerLink
Log in

Codimension 1 and 2 immersions of lens spaces

  • Conference paper
  • First Online:
Differential Geometry and Topology

Part of the book series: Lecture Notes in Mathematics ((2803,volume 1369))

Abstract

The existence and classification problems of codimension 1 and 2 immersions of lens spaces in Euclidean spaces have been solved completely. Also, the ring structures of

(Ln(p)) for n≦3 are determined.

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 44.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 59.95
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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Li Bang-He, Codimension 1 and 2 immersions of Dold manifold in Euclidean space, Kexue Tongbao, 1987.

    Google Scholar 

  2. Mahammed,N. Piccinini, R. and Suter, U., Some Applications of Topological K-Theory, North-Holland Publishing Company, 1980.

    Google Scholar 

  3. Kobayashi, T. and Sugawara, M., K^-rings of Lens spaces Ln(4), Hiroshima Math. J.

    Google Scholar 

  4. Wu Zhende, KO-rings and J-groups of Ln(8), Acta Math. Sinica 25(1982) p.49–60.

    MathSciNet  MATH  Google Scholar 

  5. Kambe, T., The structure of K^-rings of Lens spaces and their applications, Math. Soc. Japan. 1966, 135–146.

    Google Scholar 

  6. Milnor J. W. and Stasheff J. D., Characteristic Classes, Ann. of Math. Studies No. 76, 1974.

    Google Scholar 

  7. Mahammed, N., A propos de la K-theorie des espaces lenticulaires, C. R., Acad. Sci. Paris 271 (1970), 639–642.

    MathSciNet  MATH  Google Scholar 

  8. Denis Sjerve, Vector bundles over orbit manifolds, Trans. Amer. Math. Soc. 138 (1969), 97–106.

    Article  MathSciNet  MATH  Google Scholar 

  9. Mahammed, N., K-theorie des espaces lenticulaires. C. R. Acad. Sci. Paris 272 (1971), p. 1363–1365.

    MathSciNet  MATH  Google Scholar 

  10. Li Bang-He, Parallelizability of algebraic knots and canonical framings, Scientia Sinica, 27 (1984), 1164–1171.

    MathSciNet  MATH  Google Scholar 

  11. Hirsch, M., Immersions of manifolds, Trans. Amer. Math. Soc. 93 (1959), 242–276.

    Article  MathSciNet  MATH  Google Scholar 

  12. James, I. and Thomas, E., Classifying of sections, Topology 4 (1966), 351–359

    Article  MathSciNet  MATH  Google Scholar 

  13. Li Bang-He, On immersions of m-manifolds in (m+1)-manifolds. Math. Z. 182 (1983), 311–320.

    Article  MathSciNet  MATH  Google Scholar 

  14. Li Bang-He, On reflection of codimension 2 immersions in Euclidean spaces. Scientia Sinica (Chinese version), (1987), 793–799. (English version will be published later).

    Google Scholar 

  15. Hans J. Baues, Obstruction Theory, Lecture Notes in Math. No. 628, Springer-Verlag, 1977.

    Google Scholar 

  16. Kervaire, M., Some nonstable homotopy groups of Lie groups, Illinois J. of Math., 4(1960), 161–169.

    MathSciNet  MATH  Google Scholar 

  17. Wu Wen-Tsun, On the immersions of C∞-3-manifolds in a Euclidean space, Scientia Sinica, 13(1964), 335–336.

    MathSciNet  MATH  Google Scholar 

  18. Li Bang-He, On classification of immersions of n-manifolds in (2n-1)-manifolds, Comment Math. Helv. 57(1982), 135–144.

    Article  MathSciNet  Google Scholar 

  19. Ewing J., Moolgavkar S. and Smith L., Stable parallelizability of Lens spaces, J. Pure & Applied Algebra, 10(1977), 177–191.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Systems Science, Academia Sinica, Beijing, China

    Bang-He Li

  2. Dept. of Math. Graduate School of Academia Sinica, Beijing, China

    Zizhou Tang

Authors
  1. Bang-He Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zizhou Tang
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Boju Jiang Chia-Kuei Peng Zixin Hou

Rights and permissions

Reprints and permissions

Copyright information

© 1989 Springer-Verlag

About this paper

Cite this paper

Li, BH., Tang, Z. (1989). Codimension 1 and 2 immersions of lens spaces. In: Jiang, B., Peng, CK., Hou, Z. (eds) Differential Geometry and Topology. Lecture Notes in Mathematics, vol 1369. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0087531

Download citation

  • DOI: https://doi.org/10.1007/BFb0087531

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-51037-6

  • Online ISBN: 978-3-540-46137-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation