Skip to main content
SpringerLink
Log in

Classification of pairs of Arf functions on orientable and nonorientable surfaces

  • Published:
Functional Analysis and Its Applications Aims and scope

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. B. A. Dubrovin, S. P. Novikov, and A. T. Fomenko, Modern Geometry [in Russian], Nauka, Moscow (1985).

    Google Scholar 

  2. Yu. I. Manin, “Superalgebraic curves and quantum strings,” Trudy Mat. Inst. Steklov.,183, 126–138 (1990).

    Google Scholar 

  3. J. Milnor and D. Husemoller, Symmetric Bilinear Forms, Springer-Verlag, New York (1973).

    Google Scholar 

  4. S. M. Natanzon, “Moduli of real algebraic curves,” Tr. Mosk. Mat. Obshch.,37, 219–253 (1978).

    Google Scholar 

  5. S. M. Natanzon, “Moduli spaces of super-Riemann supersurfaces,” Mat. Zametki,45, No. 4, 111–116 (1989).

    Google Scholar 

  6. S. M. Natanzon, “Klein supersurfaces,” Mat. Zametki,48, No. 2, 72–82 (1990).

    Google Scholar 

  7. S. M. Natanzon, “Klein surfaces,” Usp. Mat. Nauk,45, No. 6, 47–90 (1990).

    Google Scholar 

  8. S. M. Natanzon, “Topological classification of pairs of spinor forms on surfaces,” Usp. Mat. Nauk,47, No. 1, 215–216 (1992).

    Google Scholar 

  9. V. A. Rokhlin, “New results in the theory of four-dimensional manifolds,” Dokl. Akad. Nauk SSSR,84, 221–224 (1952).

    Google Scholar 

  10. C. Arf, “Untersuchungen uber quadratische Formen in Korpern der Charakteristik 2,” J. Reine Angew. Math.,183, 148–167 (1941).

    Google Scholar 

  11. M. Atiyah, “Riemann surfaces and spin structures,” Ann. Sci. École Norm. Sup. (4) Ser. 1,4 (1971).

  12. S. V. Chmutov, “Monodromy groups of critical point of functions,” Invent. Math.,73, 491–510 (1983).

    Google Scholar 

  13. M. Dehn, “Die Gruppe der Abbildungsklassen,” Acta Math.,69 (1938).

  14. A. Krazer, Lehrbuch der Thetafunktionen, Lpz. (1903).

  15. M. I. Monastyrsky and S. M. Natanzon, “The moduli space of superconformal instantons in sigma models,” Mod. Phys. Lett. A,6, No. 19, 1787–1796 (1991).

    Google Scholar 

  16. D. Mumford, “Theta characteristics of an algebraic curve,” Ann. Sci. École Norm. Sup. (4) Ser. 2,4, 181–192 (1971).

    Google Scholar 

  17. S. M. Natanzon, “Moduli spaces in RiemannN = 1 andN = 2 supersurfaces,” J. Geom. Phys.,12, 35–54 (1993).

    Google Scholar 

  18. R. Robertello, “An invariant of knot cobordism,” Comm. Pure Appl. Math.,18, 543–555 (1965).

    Google Scholar 

  19. W. Scherrer, “Zur Theorie der endlichen Gruppen topologischer Abbindungen von geschlossenen Flachen in sich,” Comment. Math. Helv.,1, 69–119 (1929).

    Google Scholar 

  20. J. P. Serre, “Revetements à ramification impaire et thêta-caracteristiques,” C. R. Acad. Sci. Paris Ser. I,311, 547–552 (1990).

    Google Scholar 

Download references

Authors
  1. S. M. Natanzon
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Moscow Independent University. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 28, No. 3, pp. 35–46, July–September, 1994.

The research described in this publication was made possible in part by Grant No. MD8000 from the International Science Foundation.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Natanzon, S.M. Classification of pairs of Arf functions on orientable and nonorientable surfaces. Funct Anal Its Appl 28, 178–186 (1994). https://doi.org/10.1007/BF01078451

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01078451

Keywords

Search

Navigation