Rocky Mountain Journal of Mathematics

The number of minimal components and homologically independent compact leaves of a weakly generic Morse form on a closed surface

I. Gelbukh

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Article information

Source
Rocky Mountain J. Math. Volume 43, Number 5 (2013), 1537-1552.

Dates
First available in Project Euclid: 25 October 2013

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1382705668

Digital Object Identifier
doi:10.1216/RMJ-2013-43-5-1537

Mathematical Reviews number (MathSciNet)
MR3127837

Zentralblatt MATH identifier
1280.57021

Subjects
Primary: 57R30: Foliations; geometric theory 58K65: Topological invariants

Keywords
Surface Morse form foliation number of minimal components

Citation

Gelbukh, I. The number of minimal components and homologically independent compact leaves of a weakly generic Morse form on a closed surface. Rocky Mountain J. Math. 43 (2013), no. 5, 1537--1552. doi:10.1216/RMJ-2013-43-5-1537. https://projecteuclid.org/euclid.rmjm/1382705668


Export citation

References

  • Pierre Arnoux and Gilbert Levitt, Sur l'unique ergodicité des 1-formes fermées singulières, Invent. Math. 84 (1986), 141-156.
  • Michael Farber, Topology of closed one-forms, Math. Surv. 108, American Mathematical Society, 2004.
  • Irina Gelbukh, Presence of minimal components in a Morse form foliation, Diff. Geom. Appl. 22 (2005), 189-198.
  • –––, Number of minimal components and homologically independent compact leaves for a Morse form foliation, Stud. Sci. Math. Hung. 46 (2009), 547-557.
  • –––, On the structure of a Morse form foliation, Czech. Math. J. 59 (2009), 207-220.
  • –––, Structure of a Morse form foliation on a closed surface in terms of genus, Diff. Geom. Appl. 29 (2011), 473-492.
  • Frank Harary, Graph theory, Addison-Wesley Publishing Company, Massachusetts, 1994.
  • Hideki Imanishi, On codimension one foliations defined by closed one forms with singularities, J. Math. Kyoto Univ. 19 (1979), 285-291.
  • Anatole Katok, Invariant measures for flows on oriented surfaces, Sov. Math. Dokl. 14 (1973), 1104-1108.
  • Artemiy Grigorievich Maier, Trajectories on closed orientable surfaces, Math. Sbor. 12 (1943), 71-84.
  • Irina Mel'nikova, An indicator of the noncompactness of a foliation on $M^2_g$, Math. Notes 53 (1993), 356-358.
  • –––, A test for non-compactness of the foliation of a Morse form, Russ. Math. Surv. 50 (1995), 444-445.
  • –––, Maximal isotropic subspaces of skew-symmetric bilinear mapping, Moscow Univ. Math. Bull. 54 (1999), 1-3. \noindentstyle