Skip to main content
SpringerLink
Log in

Produktzerlegung und Äquivalenz von Raumkeimen I Der allgemeine Fall

  • III Section — Several Complex Variables
  • Conference paper
  • First Online:
Complex Analysis — Fifth Romanian-Finnish Seminar

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1014))

Abstract

As an application of [19] we generalise Ehpraims product-structure-theorems for irreducible complex-analytic germs in [4], [5], [6] to relative arbitrary germs of spaces with arbitrary classes of differentiability, including all complex analytic, real analytic, semi-analytic or sub-analytic germs. This opens a way to generalise Ephraims C∞-classification of irreducible complex analytic germs ([21]).

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 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.

Literatur

  1. Campo, N.A': Le nombre de Lefschetz d'une monodromie. Indag. Math. 35 (1973), 113–118

    Article  MathSciNet  MATH  Google Scholar 

  2. Becker, J.: Ck and analytic equivalence of complex analytic Varieties, Math. Ann. 225, (1977), 57–67

    Article  MathSciNet  MATH  Google Scholar 

  3. Bloom, T.: C1-functions on a complex analytic variety. Duke Math. J. 36 (1969), 283–296

    Article  MathSciNet  MATH  Google Scholar 

  4. Ephraim, R.: C∞ and analytic equivalence of singularities. Proc. of Conference of Complex Analysis 1972, Rice Univ. Studies

    Google Scholar 

  5. Ephraim, R.: The cartesian product structure of singularities. Trans. Amer. Math. Soc. 224, (1976), 299–311

    MathSciNet  MATH  Google Scholar 

  6. Ephraim, R.: Cartesian product structure of singularities. Proc. of Symp. in pure Math., 30 (1977), 21–23

    Article  MathSciNet  MATH  Google Scholar 

  7. Gibson, C.G.; Wirthmüller, K.; Plessis, A.A. du; Looijenga, E.J.N.: Topological stability of smooth mappings Springer Lecture Notes in Math., 552 (1977)

    Google Scholar 

  8. Gottschling, E.: Invarianten endlicher Gruppen und biholomorphe Abbildungen. Inv. Math. 6 (1969), 315–326

    Article  MathSciNet  MATH  Google Scholar 

  9. Hironáka, H.: Subanalytic sets. Number Theory, Algebraic Geometry and Commutative Algebra. In honour of Y. Akizuki, Kinokuniya, Tokio (1973), p 453–493

    Google Scholar 

  10. Lojasiewicz, S.: Ensembles semi-analytic, polycopie IHES (1965)

    Google Scholar 

  11. Milnor, J.: Singular points of complex hypersurfaces. Annales of Math. Studies No. 61, New York, Princeton Univ. Press 1968

    MATH  Google Scholar 

  12. Mumford, D.: The topology of normal singularities of an algebraic surface and a criterion for simplicity. IHES No. 9 (1961), 5–22

    Google Scholar 

  13. Prill, D.: Local classification of quotients of complex manifolds. Dukemath. Journ. 34 (1967), 375–386

    Article  MathSciNet  MATH  Google Scholar 

  14. Reichard, K.: C∞-Diffeomorphismen semi-und subanalytischer Mengen. Erscheint in Compositio Mathematica, 1981

    Google Scholar 

  15. Reichard, K.: Lokale Klassifikation von Quotientens ingularitäten reeller Mannigfaltigkeiten nach diskreten Gruppen. preprint Bochum

    Google Scholar 

  16. Reichard, K.: Produktzerlegung von Quotientensingularitäten, preprint Bochum

    Google Scholar 

  17. Spallek, K.: Über Singularitäten analytischer Mengen. Math. Ann. 172, (1967), 249–268

    Article  MathSciNet  MATH  Google Scholar 

  18. Spallek, K.: Differenzierbare Räume. Math. Ann. 180 (1969), 269–296

    Article  MathSciNet  MATH  Google Scholar 

  19. Spallek, K.: Geometrische Bedingungen für die Integrabilität von Vektorfeldern auf Teilmengen des Rn. manuscripta math. 25 (1978), 147–160

    Article  MathSciNet  MATH  Google Scholar 

  20. Spallek, K.: L-platte Funktionen auf semianalytischen Mengen. Math. Ann. 227 (1977), 277–286

    Article  MathSciNet  MATH  Google Scholar 

  21. Spallek, K.: Produktzerlegung und Äquivalenz von Raumkeimen II.

    Google Scholar 

  22. Spallek, K.: Differenzierbare und analytische Struktur auf analytischen und semianalytischen Räumen. preprint

    Google Scholar 

  23. Strub, R.: Vollständige Klassifikation der Singularitäten von Quotienten von unendlich oft reell-differenzierbaren Mannigfaltigkeiten nach eigentlich diskontinuierlichen Gruppen. Dissertation, Mainz (1980)

    Google Scholar 

  24. Thom, R.: Ensembles et morphismes stratifies. Bull. Amer. Math. Soc. 75 (1969), 496–549

    Article  MathSciNet  MATH  Google Scholar 

  25. Wavrik, J.J.: A theorem on solutions of analytic equations with applications to deformations of complex structures. Math.Am. 216 (1975), 127–142

    MathSciNet  MATH  Google Scholar 

  26. Whitney, H.: Tangents to an analytic variety. Am. of Math. 81 (1965), 496–549

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Ruhr-Universität Bochum Fachbereich Mathematik, Universitätsstr. 150, D 4630, Bochum 1

    K. Spallek

Authors
  1. K. Spallek
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Cabiria Andreian Cazacu Nicu Boboc Martin Jurchescu Ion Suciu

Rights and permissions

Reprints and permissions

Copyright information

© 1983 Springer-Verlag

About this paper

Cite this paper

Spallek, K. (1983). Produktzerlegung und Äquivalenz von Raumkeimen I Der allgemeine Fall. In: Cazacu, C.A., Boboc, N., Jurchescu, M., Suciu, I. (eds) Complex Analysis — Fifth Romanian-Finnish Seminar. Lecture Notes in Mathematics, vol 1014. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0072072

Download citation

  • DOI: https://doi.org/10.1007/BFb0072072

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-12683-6

  • Online ISBN: 978-3-540-38672-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation