Skip to main content

Extensions of the Gudkov-Rohlin congrunce

  • Algebraic Varieties
  • Chapter
  • First Online:
Topology and Geometry — Rohlin Seminar

Part of the book series: Lecture Notes in Mathematics ((2179,volume 1346))

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

eBook
USD 16.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 69.95
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. Arnold V.I. On the arrangement of the ovals of real plane curves, involutions of 4-simensional smooth manifolds and the arithmetic of integral quadratic forms.-Funkc.Anal i Prilož, 5, 1971, N 3, 1–9.

    Google Scholar 

  2. Barge J., Lannes J., Latour Fr., Vogel P. Λ-sphéres.-Ann.Sci. Ecole Norm.Super. (4) 7, 1974, 463–505 (1975).

    MathSciNet  MATH  Google Scholar 

  3. van der Blij. An invariant of quadratic forms mod 8.-Indag. Math., 21, 1959, 291–293.

    Article  MathSciNet  MATH  Google Scholar 

  4. Fiedler T. Now congruences in topology of real plane algebraic curves.-Dokl.Akad.Nauk SSSR, 270, 1983, N 1, 56–58.

    MathSciNet  Google Scholar 

  5. Gudkov D.A., Utkin G.A. Topology of curves of 6 order and surfaces of 4 order,-Uchen.Zap.Gor’kov.Univ.,87, 1969.

    Google Scholar 

  6. Gudkov D.A., Krachnov A.D. On the periodicity of the Euler characteristic of real algebraic (M-1)-manifolds.-Funkc.Anal. i Prilož., 7, 1973, N 2, 15–19.

    MathSciNet  Google Scholar 

  7. Guillou L., Marin A. Une extension d’un théorem de Rohlin sur la signature.-Compt.Rendus, 285, 1977, N 3, 95–97.

    MathSciNet  MATH  Google Scholar 

  8. Kharlamov V.M. New congruences for the Euler characteristic of real algebraic manifolds.-Funkc.Anal. i Priloz., 7, 1973, N 2, 74–78.

    MathSciNet  Google Scholar 

  9. Kharlamov V.M., Viro O.Ya. Congruences for real algebraic curves with singularities.-Uspehi Mat.Nauk, 35, 1980, N 4, 154–155.

    Google Scholar 

  10. Khovanskij A.G. Fewnomials and Pfaff manifolds.-Proc.Int.Cong. Math 16–24 1983 Warsawa, 549–564, 1984.

    Google Scholar 

  11. Korchagin A.B. Isotopic classification of plane seventh degree curves with the only singular point Z15, this volume.

    Google Scholar 

  12. Marin A. Quelques remarques sur les courber algébriques planes reelles.-Publ.Math.Univ.Paris VII, 9, 1980, 51–68.

    Google Scholar 

  13. Nikulin V.V. Involutions of integral quadratic forms and their applications to real algebraic geometry.-Izv.Akad.Nauk SSSR, ser. matem., 47, 1983, N 1, 109–188.

    MathSciNet  Google Scholar 

  14. Polotovskij G.M. Cataloque of M-splitting curves of 6 order.-Dokl.Akad.Nauk SSSR, 236, 1977, N 3, 548–551; see also Complete classification of M-splitting curves of 6 order in ℝP2.-paper placed in VINITI, 20.04.78, N 349-78DEP.

    MathSciNet  Google Scholar 

  15. Polotovskij G.M. On the classification of the non-singular curves of degree8.-this volume.

    Google Scholar 

  16. Rohlin V.A. Proof of Gudkov’s conjecture.-Funkc.Anal. i Priloz. 6, 1972, N 2, 62–64.

    MathSciNet  Google Scholar 

  17. Rohlin V.A. Congruences modulo 16 in Hilbert’s sixteenth problem.-Funkc.Anal. i Priloz, 6, 1972, N 4, 58–64.

    MathSciNet  Google Scholar 

  18. Rohlin V.A. Congruences modulo 16 in Hilbert’s sixteenth problem, II.-Funkc.Anal. i Prilož., 7, 1973, N 2, 91–92.

    Article  MathSciNet  Google Scholar 

  19. Rohlin V.A. Complex topological characteristics of real algebraic curves.-Uspehi Mat.Nauk, 33, 1978, N 5, 77–89.

    MathSciNet  Google Scholar 

  20. Shustin E.I. The Hilbert-Rohn method and smoothings of singular points of real algebraic curves.-Dokl.Akad.Nauk SSSR, 281,1985, N 1, 33–36.

    MathSciNet  Google Scholar 

  21. Viro O.Ya. Progress in topology of real algebraic manifolds over the last 6 years.-Uspehi Mat.Nauk, 41, 1986, N 3, 45–67.

    MathSciNet  Google Scholar 

  22. Viro O.Ya. Gluing of plane real algebraic curves and constructions of curves of degrees 6 and 7.-Lect.N.Math., 1060, 1984, 187–200.

    Article  MathSciNet  MATH  Google Scholar 

  23. Viro O.Ya. Gluing of algebraic hypersurfaces smoothings of singularities and constructions of curves.-Proc.Leningrad Int.Topological Conf., 1983, 149–197.

    Google Scholar 

  24. Wilson G. Hilbert’s sixteenth problem.-Topology, 17, 1978,53–73.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Oleg Yanovich Viro Anatoly Moiseevich Vershik

Rights and permissions

Reprints and permissions

Copyright information

© 1988 Springer-Verlag

About this chapter

Cite this chapter

Kharlamov, V.M., Viro, O.Y. (1988). Extensions of the Gudkov-Rohlin congrunce. In: Viro, O.Y., Vershik, A.M. (eds) Topology and Geometry — Rohlin Seminar. Lecture Notes in Mathematics, vol 1346. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0082784

Download citation

  • DOI: https://doi.org/10.1007/BFb0082784

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-50237-1

  • Online ISBN: 978-3-540-45958-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics