## 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

#### Article information

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

Dates
First available in Project Euclid: 25 October 2013

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

#### 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

#### 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