Skip to main content

Surgering the equatorial immersion in law dimensions

  • Immersions And Vector Bundle Morphisms
  • Conference paper
  • First Online:
Differential Topology

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1350))

Abstract

More examples of immersions with one 0-dimensional multiple point are given in three and four space. Given an immersion in four space with one 0-dimensional multiple point, a geometric obstruction to finding an immersion in five space with the same property is given. A series of proposed geometric constructions is given. Completing each of these constructions will lead to further insight to Eccles's theorem and the Kervaire invariant problem.

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 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. Carter, J. Scott, “Surgery Theory of Immersions”, Proc. Northwestern Homotopy Theory Conf. (Miller and Priddy, eds), AMS Contemp. Math Series, 19 (1983), 23–37.

    Google Scholar 

  2. Carter, J. Scott, “Surgery on Codimension One Immersions in (n+1)-space: Removing n-tuple points”, Trans. AMS 298, No. 1, (Nov 1986), 83–102.

    MATH  Google Scholar 

  3. Carter, J. Scott, “On Generalizing Boy's Surface: Constructing a Generator of the Third Stable Stem”, Trans. AMS 298, No. 1, (Nov 1986), 103–122

    MATH  Google Scholar 

  4. Carter, J. Scott, “A Further Generalization of Boy's Surface”, Houston Journal of Mathematics 12, No. 1 (1986), 11–31.

    MathSciNet  MATH  Google Scholar 

  5. Carter, J. Scott, “Simplifying the Self Intersection Sets of Codimension One Immersions in (n+1)-space”, The Houston Journal of Mathematics, 13, No. 3 (1987), 353–366.

    MATH  Google Scholar 

  6. Carter, J. Scott, “Surgery on the Equatorial Immersion I”, to appear in Illinois Journal of Mathematics (circa 1988).

    Google Scholar 

  7. Eccles, Peter J. “Multiple Points of Codimension Immersions of Oriented Manifolds”, Math. Proc. Cambr. Phil. Soc. 87 (1980), 213–220.

    Article  MathSciNet  MATH  Google Scholar 

  8. Eccles, Peter J., “Codimension One Immersions and the Kervaire Invariant One Problem”, Math Proc. Cambr. Phil. Soc. 90 (1981), 483–493.

    Article  MathSciNet  MATH  Google Scholar 

  9. Kervaire, Michel, “On G. Whitehead Generalized Hopf Invariant”, Annals of Math 69, No. 2, (1959), 345–364.

    Article  MathSciNet  MATH  Google Scholar 

  10. Koschorke, Ulrich, “Multiple points of Immersions and the Kahn-Priddy Theorem”, Math. Z., 169, 223–236.

    Google Scholar 

  11. Koschorke, Ulrich, Personal notes.

    Google Scholar 

  12. Lannes, J., “Sur les Immersions de Boy”, (preprint circa 1982).

    Google Scholar 

  13. Sato, N., “Cobordism of Semi-boundary Links”, Topology and Its Applications 18 (1984), 225–235.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Ulrich Koschorke

Rights and permissions

Reprints and permissions

Copyright information

© 1988 Springer-Verlag

About this paper

Cite this paper

Carter, J.S. (1988). Surgering the equatorial immersion in law dimensions. In: Koschorke, U. (eds) Differential Topology. Lecture Notes in Mathematics, vol 1350. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0081473

Download citation

  • DOI: https://doi.org/10.1007/BFb0081473

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-50369-9

  • Online ISBN: 978-3-540-45990-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics