The BIC of a singular foliation defined by an abelian group of isometries

Martintxo Saralegi-Aranguren, and Robert Wolak. "The BIC of a singular foliation defined by an abelian group of isometries." Annales Polonici Mathematici 89.3 (2006): 203-246. <http://eudml.org/doc/280737>.

@article{MartintxoSaralegi2006,
abstract = {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 $ℍ*_\{p̅\}(M/ℱ)$ 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).},
author = {Martintxo Saralegi-Aranguren, Robert Wolak},
journal = {Annales Polonici Mathematici},
keywords = {conical foliation; isometric action; basic intersection cohomology},
language = {eng},
number = {3},
pages = {203-246},
title = {The BIC of a singular foliation defined by an abelian group of isometries},
url = {http://eudml.org/doc/280737},
volume = {89},
year = {2006},
}

TY - JOUR
AU - Martintxo Saralegi-Aranguren
AU - Robert Wolak
TI - The BIC of a singular foliation defined by an abelian group of isometries
JO - Annales Polonici Mathematici
PY - 2006
VL - 89
IS - 3
SP - 203
EP - 246
AB - 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 $ℍ*_{p̅}(M/ℱ)$ 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).
LA - eng
KW - conical foliation; isometric action; basic intersection cohomology
UR - http://eudml.org/doc/280737
ER -