The deficiency of a cohomology class
Author:
C. A. Morales
Journal:
Proc. Amer. Math. Soc. 138 (2010), 43214329
MSC (2000):
Primary 37C10; Secondary 37C50
Published electronically:
May 24, 2010
MathSciNet review:
2680058
Fulltext PDF
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Abstract: We define the deficiency of a cohomology class with respect to a vector field as the set of limit points in the ambient manifold of long almost closed orbits representing homology classes on which is nonpositive. We prove that, up to infinite cyclic coverings, the sole vector fields on closed manifolds exhibiting nonzero cohomology classes with finite deficiency are the gradientlike ones. We also prove that if the manifold is not a sphere, every singularity is hyperbolic and there is a closed transverse submanifold intersecting all regular orbits, then there is also a nonzero cohomology class with finite deficiency.
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Additional Information
C. A. Morales
Affiliation:
Instituto de Matemática, Universidade Federal do Rio de Janeiro, P. O. Box 68530, 21945970 Rio de Janeiro, Brazil
Email:
morales@impa.br
DOI:
http://dx.doi.org/10.1090/S000299392010104331
Keywords:
Cohomology class,
deficiency,
vector field
Received by editor(s):
October 28, 2009
Received by editor(s) in revised form:
February 1, 2010
Published electronically:
May 24, 2010
Additional Notes:
This research was partially supported by CNPq, FAPERJ and PRONEXBrazil
Communicated by:
Daniel Ruberman
Article copyright:
© Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
