Skip to main content
Log in

On the van Kampen-Flores theorem

  • Published:
Mathematical Notes Aims and scope Submit manuscript

Abstract

In this paper we generalize the van Kampen-Flores theorem for mappings of a simplex into a topological manifold.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. E. R. Van Kampen, “Komplexe in euklidischen Raumen,”Abh. Math. Sem. Hamburg.,9, 72–78 (1932).

    MATH  Google Scholar 

  2. A. Flores, “Übern-dimensionale Komplexe die imR 2n+1 absolut selbstverschlungen sind,”Ergeb. Math. Kolloq.,6, 4–7 (1933–34).

    Google Scholar 

  3. J. Radon, “Mengen konvexer Körper, die einen gemeinsamen Punkt enthalten,”Math. Ann.,83, 113–115 (1921).

    Article  MATH  MathSciNet  Google Scholar 

  4. E. G. Bajmóczy and I. Bárány, “On a common generalization of Borsuk's and Radon's theorem,”Acta Math. Acad. Sci. Hungar.,34, 347–350 (1979).

    Article  MathSciNet  Google Scholar 

  5. H. Tverberg, “A generalization of Radon's theorem,”J. London Math. Soc.,41, 123–128 (1966).

    MATH  MathSciNet  Google Scholar 

  6. I. Bárány, S. B. Shlossman and A. Szücs, “On topological generalization of a theorem of Tverberg,”J. London Math. Soc.,23, 158–164 (1981).

    MathSciNet  Google Scholar 

  7. K. S. Sarkaria, “A generalized van Kampen-Flores theorem,”Proc. Amer. Math. Soc.,111, No. 2, 559–565 (1991).

    MATH  MathSciNet  Google Scholar 

  8. K. S. Sarkaria, “A generalized Kneser conjecture,”J. Combin. Theory. Ser. B.,49, 236–240 (1990).

    Article  MATH  MathSciNet  Google Scholar 

  9. Wu Yi Hsiang,Cohomology Theory of Topological Transformation Groups, Springer-Verlag, Berlin-Heidelberg-New York (1975).

    Google Scholar 

  10. C. T. Yang, “On theorems of Borsuk-Ulam, Kakutani-Yamabe-Yujobo, and Dyson. I,”Ann. of Math.,60, 262–282 (1954).

    MATH  MathSciNet  Google Scholar 

  11. A. S. Shvarts, “Some estimates of the genus of topological space in Krasnosel'skii sense,”Uspekhi Mat. Nauk [Russian Math. Surveys],12, No. 4, 209–214 (1957).

    MATH  Google Scholar 

  12. A. S. Shvarts, “The genus of fibered space,”Trudy Moskov. Mat. Obshch. [Trans. Moscow Math. Soc.],11, 99–126, (1962).

    MATH  Google Scholar 

  13. P. E. Conner and E. E. Floyd, “Fixed point free involutions and equivariant maps,”Bull. Amer. Math. Soc.,66, 416–441 (1960).

    MathSciNet  Google Scholar 

  14. A. Yu. Volovikov, “Bourgain-Yang-like theorem for ℤ n p -action,”Mat. Sb. [Math. USSR-Sb.],183, No. 7, 115–144 (1992).

    MATH  Google Scholar 

  15. I. Kriz, “Equivariant cohomology and lower bounds for chromatic numbers,”Trans. Amer. Math. Soc.,333, No. 2, 567–577 (1992).

    MATH  MathSciNet  Google Scholar 

  16. H. J. Munkholm, “On the Borsuk-Ulam theorem for ℤ p α actions onS 2n−1 and mapsS 2n−1 → ℝm,”Osaka J. Math.,7, 451–456 (1970).

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Translated fromMatematicheskie Zametki, Vol. 59, No. 5, pp. 663–670, May, 1996.

This research was supported by the International Science Foundation under grant No. JH2100.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Volovikov, A.Y. On the van Kampen-Flores theorem. Math Notes 59, 477–481 (1996). https://doi.org/10.1007/BF02308813

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02308813

Keywords

Navigation