Skip to main content

Lectures on immersion theory

  • 732 Accesses

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

Keywords

  • Vector Bundle
  • Braid Group
  • Obstruction Theory
  • Twisted Product
  • Whitney Class

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   44.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   59.95
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. J.F. Adams, “Stable Homotopy and Generalized Homology,” Mathematical Lecture Notes, University of Chicago, 1971.

    Google Scholar 

  2. J.W. Alexander, Topological invariants of knots and links, Trans. A.M.S. 30 (1928), 275–306.

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. E. Artin, Theorie der Zöpfe, Hamburg Abh. 4 (1925), 47–72.

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. M.F. Atiyah, Thom complexes, Proc. Lond. Math. Soc. (3) 11 (1961), 291–310.

    CrossRef  MathSciNet  MATH  Google Scholar 

  5. J. Birman, “Braids, Links, and Mapping Class Groups,” Annals of Math. Studies 82, Princeton Univ. Press, 1974.

    Google Scholar 

  6. A. Bousfield, E. Curtis, D. Kan, D. Quillen, D. Rector, and J. Schlesinger, The mod p lower central series and the Adams spectral sequence, Topology 5 (1966), 331–342.

    CrossRef  MathSciNet  MATH  Google Scholar 

  7. W. Browder, The Kervaire invariant of framed manifolds and its generalizations, Annals of Math. 90 (1969), 157–186.

    CrossRef  MathSciNet  MATH  Google Scholar 

  8. E.H. Brown, Cohomology theories, Annals of Math. 75 (1962), 467–484.

    CrossRef  MathSciNet  MATH  Google Scholar 

  9. E.H. Brown and R.L. Cohen, The Adams spectral sequence of Ω 2 S 3 and Brown-Gitler spectra, Annals of Math. Studies 113 (1987), 101–125.

    MathSciNet  Google Scholar 

  10. E.H. Brown and S. Gitler, A spectrum whose cohomology is a certain cyclic module over the Steenrod algebra, Topology 12 (1973), 283–295.

    CrossRef  MathSciNet  MATH  Google Scholar 

  11. E.H. Brown and F.P. Peterson, Relations among characteristic classes I, Topology 3 (1964), 39–52.

    CrossRef  MathSciNet  MATH  Google Scholar 

  12. —, On immersions of n-manifolds, Advances in Math. 24 (1977), 74–77.

    CrossRef  MathSciNet  MATH  Google Scholar 

  13. —, On the stable decomposition of Ω 2 S r+2, Trans. A.M.S. 243 (1978), 287–298.

    CrossRef  MathSciNet  MATH  Google Scholar 

  14. —, A universal space for normal bundles of n-manifolds, Comment. Math. Helv. 54 (1979), 405–430.

    CrossRef  MathSciNet  MATH  Google Scholar 

  15. R.L. Brown, Immersions and embeddings up to cobordism, Canad. J. Math. (6) 23 (1971), 1102–1115.

    CrossRef  MathSciNet  MATH  Google Scholar 

  16. S. Bullett, Braid orientations and Stiefel-Whitney classes, Quart. J. Math. Oxford 2 (1981), 267–285.

    CrossRef  MathSciNet  MATH  Google Scholar 

  17. F.R. Cohen, Braid orientations and bundles with flat connections, Invent. Math. 46 (1978), 99–110.

    CrossRef  MathSciNet  MATH  Google Scholar 

  18. ___, Artin's braid groups and classical homotopy theory, Contemp. Math. 44 (1985), 207–219.

    CrossRef  MATH  Google Scholar 

  19. F.R. Cohen, T. Lada, and J.P. May, “The Homology of Iterated Loop Spaces,” Lecture Notes 533, Springer Verlag, New York, 1976.

    MATH  Google Scholar 

  20. R.L. Cohen, The geometry of Ω 2 S 3 and braid orientations, Invent. Math. 54 (1979), 53–67.

    CrossRef  MathSciNet  Google Scholar 

  21. ___, Representations of Brown-Gitler spectra, Proc. Top. Symp. at Siegen, 1979, Lecture Notes 788, Springer Verlag, New York (1980), 399–417.

    CrossRef  Google Scholar 

  22. ___, Odd primary infinite families in stable homotopy theory, Memoirs of A.M.S. 242 (1981).

    Google Scholar 

  23. ___, The homotopy theory of immersions, Proc. Int. Cong. of Math., Warszawa 1982 1 (1984), 627–640.

    MathSciNet  Google Scholar 

  24. ___, The immersion conjecture for differentiable manifolds, Annals of Math. 122 (1985), 237–328.

    CrossRef  MathSciNet  MATH  Google Scholar 

  25. R.L. Cohen, J.D.S. Jones, and M. Mahowald, The Kervaire invariant of immersions, Inven. Math. 79 (1985), 95–123.

    CrossRef  MathSciNet  MATH  Google Scholar 

  26. A. Dold, Erzeugende der Thomschen Algebra ν*, Math. Zeit. 65 (1956), 25–35.

    CrossRef  MathSciNet  MATH  Google Scholar 

  27. D.B. Fuks, Cohomologies of the braid groups mod 2, Functional Anal. and its Applic.. 4 (1970), 143–151.

    CrossRef  MATH  Google Scholar 

  28. V.F.R. Jones, A polynomial invariant for knots via von Neumann algebras, Bull. A.M.S. 12 (1985), 103–111.

    CrossRef  MathSciNet  MATH  Google Scholar 

  29. P.G. Goerss, A direct construction for the duals of Brown-Gitler spectra, Indiana J. of Math. 34 (1985), 733–751.

    CrossRef  MathSciNet  MATH  Google Scholar 

  30. M.W. Hirsch, Immersions of manifolds, Trans. A.M.S. 93 (1959), 242–276.

    CrossRef  MathSciNet  MATH  Google Scholar 

  31. M.W. Hirsch, “Differential Topology,” Springer Verlag, New York, 1976.

    CrossRef  MATH  Google Scholar 

  32. D. Husemoller, “Fibre Bundles,” Springer Verlag, New York, 1966.

    CrossRef  MATH  Google Scholar 

  33. J. Lannes and S. Zarati, Sur les functeurs derives de la destbilisation, C.R. Acad. Sci. Paris 296 (1983), 573–576.

    MathSciNet  MATH  Google Scholar 

  34. M. Mahowald, On obstruction theory in orientable fibre bundles, Trans. A.M.S. 110 (1964), 315–349.

    CrossRef  MathSciNet  MATH  Google Scholar 

  35. ___, A new infinite family in 2 π se , Topology 16 (1977), 249–256.

    CrossRef  MathSciNet  MATH  Google Scholar 

  36. W.S. Massey, On the Stiefel-Whitney classes of a manifold, Amer. J. Math. 82 (1960), 92–102.

    CrossRef  MathSciNet  MATH  Google Scholar 

  37. R.J. Milgram, Iterated loop spaces, Annals Math. 84 (1966), 386–403.

    CrossRef  MathSciNet  MATH  Google Scholar 

  38. J.W. Milnor, The Steenrod algebra and its dual, Annals of Math. (2) 67 (1958), 150–171.

    CrossRef  MathSciNet  MATH  Google Scholar 

  39. J.W. Milnor and J.D. Stasheff, “Characteristic Classes,” Princeton University Press, New Jersey, 1974.

    CrossRef  MATH  Google Scholar 

  40. R. Mosher and M. Tangora, “Cohomology Operations and Applications in Homotopy Theory,” Harper and Row, New York, 1968.

    MATH  Google Scholar 

  41. J.P. May, “The geometry of iterated loop spaces,” Lecture Notes 271, Springer Verlag, New York, 1972.

    MATH  Google Scholar 

  42. V. Snaith, Algebraic cobordism and K-theory, Memoirs of A.M.S. 221 (1979).

    Google Scholar 

  43. N. Steenrod, “The Topology of Fibre Bundles,” Princeton University Press, New Jersey, 1951.

    CrossRef  MATH  Google Scholar 

  44. N.E. Steenrod and D.B.A. Epstein, “Cohomology Operations,” Princeton University Press, New Jersey, 1962.

    MATH  Google Scholar 

  45. R.E. Stong, “Notes on Cobordism Theory,” Princeton University Press, New Jersey, 1968.

    MATH  Google Scholar 

  46. R. Thom, Quelques propertés globales des varietës differentiables, Comment. Math. Helv. 28 (1954), 17–86.

    CrossRef  MathSciNet  MATH  Google Scholar 

  47. G.W. Whitehead, Generalized homology theories, Trans. A.M.S. 102 (1962), 227–283.

    CrossRef  MathSciNet  MATH  Google Scholar 

  48. H. Whitney, The singularities of a smooth n-manifold in (2n-1)-space, Annals of Math. 45 (1944), 247–293.

    CrossRef  MathSciNet  MATH  Google Scholar 

  49. W.T. Wu, Classes caractéristiques et i-carrés d'une varieté, C.R. Acad. Sci. Paris 230 (1950), 508–511.

    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

© 1989 Springer-Verlag

About this paper

Cite this paper

Cohen, R.L., Tillmann, U. (1989). Lectures on immersion theory. 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/BFb0087528

Download citation

  • DOI: https://doi.org/10.1007/BFb0087528

  • 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