The dimension of the leafwise reduced cohomology
type: Item
instance of: scholarly article
title: The dimension of the leafwise reduced cohomology
zbMATH Open document ID: 0983.57018
author: Jesús A. Álvarez López
author: Gilbert Hector
published in: American Journal of Mathematics
publication date: 2002-04-19T00:00:00Z
full work available at URL: https://arxiv.org/abs/1311.3518
full work available at URL: ajm123.4.html
Mathematics Subject Classification ID: 57R30
Mathematics Subject Classification ID: 53C12
Mathematics Subject Classification ID: 55N35
zbMATH DE Number: 1657136
zbMATH Keywords: foliation
zbMATH Keywords: subfoliation
zbMATH Keywords: vector bundle
zbMATH Keywords: leafwise cohomology
zbMATH Keywords: spectral sequence
MaRDI profile type: Publication
OpenAlex ID: W2963868509
arXiv ID: 1311.3518
DOI: 10.1353/AJM.2001.0023
Recommended article: Dimension in Bredon cohomology
Recommended article: Cohomological dimension of certain algebraic varieties
Recommended article: Cohomological Dimension of Complexes
Recommended article: Cohen-Macaulay homological dimensions
Recommended article: Dimensions of l^p-cohomology groups
Recommended article: Cohomological dimension and top local cohomology modules
Recommended article: The Kodaira dimension of Lefschetz fibrations
Recommended article: Leafwise cohomology, leafwise homologies, and subfoliations
review text: The authors give geometric conditions 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 studied for homogeneous foliations with dense leaves on closed nilmanifolds.
reviewed by: Gheorghe Pitiş
description: scientific article; zbMATH DE number 1657136