We study the cohomology properties of the singular foliation ℱ determined by an action Φ: G × M → M where the abelian Lie group G preserves a riemannian metric on the compact manifold M. More precisely, we prove that the basic intersection cohomology is finite-dimensional and satisfies the Poincaré duality. This duality includes two well known situations: ∙ Poincaré duality for basic cohomology (the action Φ is almost free). ∙ Poincaré duality for intersection cohomology (the group G is compact and connected).
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap89-3-1,
author = {Martintxo Saralegi-Aranguren and Robert Wolak},
title = {The BIC of a singular foliation defined by an abelian group of isometries},
journal = {Annales Polonici Mathematici},
volume = {89},
year = {2006},
pages = {203-246},
zbl = {1107.53018},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap89-3-1}
}
Martintxo Saralegi-Aranguren; Robert Wolak. The BIC of a singular foliation defined by an abelian group of isometries. Annales Polonici Mathematici, Tome 89 (2006) pp. 203-246. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap89-3-1/