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Simple singularities of maps

Part of the Lecture Notes in Mathematics book series (LNM,volume 192)

Keywords

  • Exact Sequence
  • Vector Bundle
  • Chern Class
  • Transversality Condition
  • Trivial Bundle

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References

  1. Aitken, A.C. Note on dual symmetric functions. Proc. Edinburgh Math. Soc. (2) 2 (1931), 164–167.

    CrossRef  MATH  Google Scholar 

  2. Atiyah, M.F. Analytic cycles on complex manifolds. Topology 1 (1962).

    Google Scholar 

  3. Borel, A. et Haefliger, A. La classe d'homologie fondamentale d'un espace analytique. Bull. Soc. Math. France 89 (1961) 461–513.

    MathSciNet  MATH  Google Scholar 

  4. Cartan, H. Quelque questions de topologie. Seminaire E.N.S. (1956–57). [Exposé 7: Haefliger, A. Les singularités des applications différentiables. Exposé 8: Haefliger, A. et Kosinski, A. Un théorème de Thom sur les singularites des applications différentiables.]

    Google Scholar 

  5. Chern, S. On the multiplication in the characteristic ring of a sphere bundle. Ann. Math. (2) 49 (1948), 362–372.

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. Dieudonné, J. Foundations of Modern Analysis. Academic Press New York 1960.

    MATH  Google Scholar 

  7. Ehresmann, C. Les prolongements d'une variété différentiable: I. Calcul des jets, prolongement principal. II. L'espace des jets d'ordre r de Vn dans Vm. C.r. Acad. Sci. (Paris) 233 (1951), 598–600 et 777–779.

    MathSciNet  MATH  Google Scholar 

  8. Grothendieck, A. La théorie des classes de Chern. Bull. Soc. Math. France 86 (1958), 137–154.

    MathSciNet  MATH  Google Scholar 

  9. Levine, H.I. Singularities of differentiable mappings. This volume., pp.1–89.

    Google Scholar 

  10. Porteous, I.R. Blowing up Chern classes. Proc. Camb. Phil. Soc. 56 (1960), 118–124.

    CrossRef  MathSciNet  MATH  Google Scholar 

  11. Thom, R. Les ensembles singuliers d'une application différentiable et leurs propriétés homologiques. Séminaire de Topologie de Strasbourg, Dec, 1957.

    Google Scholar 

  12. Todd, J.A. Canonical systems on algebraic varieties. Bol. Soc. Mat. Mexicana (2) 2 (1957), 26–44.

    MathSciNet  MATH  Google Scholar 

  13. Whitney, H. Singularities of mappings of Euclidean spaces. Symposium Internacional de Topologica Algebrica, Mexico (1958), 285–301.

    Google Scholar 

  14. Boardman, J.M. Singularities of differentiable maps. Publ. Math. I.H.E.S. 33 (1967), 21–57.

    CrossRef  MathSciNet  MATH  Google Scholar 

  15. Porteous, I.R. Normal singularities of submanifolds. To appear in J. Diff. Geom.

    Google Scholar 

  16. Porteous, I.R. Todd's canonical classes. This volume.,pp.308–312.

    Google Scholar 

  17. Ronga, F. La calcul des classes duales aux singularités de Boardman d'ordre 2. A paraître dans les Commentarii Mathematici Helvetici.

    Google Scholar 

  18. Todd, J.A. Invariant and covariant systems on an algebraic variety. Proc. Lond. Math. Soc. (2) 46 (1940), 199–230.

    CrossRef  MathSciNet  MATH  Google Scholar 

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© 1971 Springer-Verlag

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Porteous, I.R. (1971). Simple singularities of maps. In: Wall, C. (eds) Proceedings of Liverpool Singularities — Symposium I. Lecture Notes in Mathematics, vol 192. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0066829

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  • DOI: https://doi.org/10.1007/BFb0066829

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  • Print ISBN: 978-3-540-05402-3

  • Online ISBN: 978-3-540-36531-0

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