Skip to main content
SpringerLink
Log in

A test for compactness of a foliation

  • Published:
Mathematical Notes Aims and scope Submit manuscript

Abstract

We investigate foliations on smooth manifolds that are determined by a closed 1-form with Morse singularities. We introduce the notion of the degree of compactness and prove a test for compactness.

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

Similar content being viewed by others

References

  1. S. P. Novikov, “The Hamiltonian formalism and a multivalued version of Morse theory,”Uspekhi Mat. Nauk [Russian Math. Surveys],37, No. 5, 3–49 (1982).

    MATH  MathSciNet  Google Scholar 

  2. S. P. Novikov, “Critical points and level surfaces of multivalued functions,” in:Trudy Mat. Inst. Steklov [Proc. Steklov Inst. Math.],166, 201–209 (1984).

    MATH  MathSciNet  Google Scholar 

  3. A. V. Zorich, “Quasiperiodic structure of level surfaces of a 1-form close to a rational one; Novikov's problem,”Izv. Akad. Nauk SSSR, Ser. Mat. [Math. USSR-Izv.],51, No. 6, 1322–1344 (1987).

    MATH  Google Scholar 

  4. T. K. T. Le, “On the structure of level surfaces of a Morse form,”Mat. Zametki. [Math. Notes],44, No. 1, 124–133 (1988).

    MathSciNet  Google Scholar 

  5. L. A. Alaniya, “On the topological structure of the level surfaces of Morse 1-forms,”Uspekhi Mat. Nauk [Russian Math. Surveys],46, No. 3, 179–180 (1991).

    MATH  MathSciNet  Google Scholar 

  6. I. A. Mel'nikova, “A noncompactness test for a foliation onM g 2,”Mat. Zametki. [Math. Notes],53, No. 3, 158–160 (1993).

    MATH  MathSciNet  Google Scholar 

  7. Henc Damir, “Ergodicity of foliations with singularities,”J. Funct. Anal.,75, No. 2 (1987).

  8. A. Dold,Lectures on Algebraic Topology, 2nd ed., Berlin, (1980).

Download references

Author information

Authors and Affiliations

  1. Moscow State University, USSR

    I. A. Mel'nikova

Authors
  1. I. A. Mel'nikova
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated fromMatematicheskie Zametki, Vol. 58, No. 6, pp. 872–877, December, 1995.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Mel'nikova, I.A. A test for compactness of a foliation. Math Notes 58, 1302–1305 (1995). https://doi.org/10.1007/BF02304889

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02304889

Keywords

Search

Navigation