The Dimension of the Leafwise Reduced Cohomology

The Dimension of the Leafwise Reduced Cohomology

Geometric conditions are given so that the leafwise reduced cohomology is of infinite dimension, especially for foliations with dense leaves on closed manifolds. The main new definition involved is the intersection number of subfoliations with "appropriate coefficients." The leafwise reduc...

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Veröffentlicht in:American journal of mathematics 2001-08, Vol.123 (4), p.607-646
Hauptverfasser: López, Jesús A. Álvarez, Hector, Gilbert
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Geometry
Homomorphisms
Leaves
Lie groups
Mathematical manifolds
Mathematical vectors
Mathematics
Riemann manifold
Topological vector spaces
Topology
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Zusammenfassung:Geometric conditions are given so that the leafwise reduced cohomology is of infinite dimension, especially for foliations with dense leaves on closed manifolds. The main new definition involved is the intersection number of subfoliations with "appropriate coefficients." The leafwise reduced cohomology is also described for homogeneous foliations with dense leaves on closed nilmanifolds.
ISSN:0002-9327
1080-6377
1080-6377
DOI:10.1353/ajm.2001.0023