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Vanishing cycles and special fibres

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Singularity Theory and its Applications

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1462))

Abstract

We show that the homotopy type of certain special fibres in a perturbation of a holomorphic function is a wedge of spheres of middle dimension. We also define a basis of the homology of the special fibre.

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References

  1. V.I. Arnol'd, S.M. Gusein Zade, A.N. Varchenko: Singularities of Differentiable Maps II, Birkhäuser, 1988.

    Google Scholar 

  2. M. Goreski, R. MacPherson: Stratified Morse Theory, Ergebnisse der Mathematik und ihrer Grenzgebiete 3.Folge, Band 14, Springer Verlag 1988.

    Google Scholar 

  3. T. de Jong, D. van Straten: Disentanglements, This Volume.

    Google Scholar 

  4. K. Lamotke: Die Homologie isolierter Singularitäten, Math. Zeitschrift 143, 27–44 (1975).

    Article  MATH  MathSciNet  Google Scholar 

  5. E.J.N. Looijenga: Isolated Singular Points on Complete Intersections, LMS-Lecture Notes Series 77, Cambridge University Press, 1984.

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  6. D.M.Q. Mond: Vanishing cycles for analytic maps, This Volume.

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  7. D. Siersma: Isolated line singularities, Proceedings of Symposia in Pure Mathematics Volume 40 (Part 2) (1983), 485–496.

    Article  MathSciNet  Google Scholar 

  8. D. Siersma: Singularities with critical locus a 1-dimensional complete intersection and transversal type A 1, Topology and its applications 27 (1987) 51–73.

    Article  MATH  MathSciNet  Google Scholar 

  9. D. Siersma: Variation Mappings on singularities with a 1-dimensional critical locus, Topology (to appear).

    Google Scholar 

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Author information

Authors and Affiliations

  1. Mathematisch Instituut, Rijksuniversiteit te Utrecht, P.O. Box 80.010, 3508 TA, Utrecht, The Netherlands

    Dirk Siersma

Authors
  1. Dirk Siersma
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David Mond James Montaldi

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© 1991 Springer-Verlag Berlin Heidelberg

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Siersma, D. (1991). Vanishing cycles and special fibres. In: Mond, D., Montaldi, J. (eds) Singularity Theory and its Applications. Lecture Notes in Mathematics, vol 1462. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0086389

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  • DOI: https://doi.org/10.1007/BFb0086389

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-53737-3

  • Online ISBN: 978-3-540-47060-1

  • eBook Packages: Springer Book Archive

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