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

• Autorzy: Martintxo Saralegi-Aranguren , Robert Wolak
• Języki publikacji: EN

Abstrakty

EN

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).

Kategorie tematyczne

• 53C12: Foliations (differential geometric aspects)
• 22Fxx: Noncompact transformation groups
• 57R30: Foliations; geometric theory
• 58A35: Stratified sets
• 55N33: Intersection homology and cohomology

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2006
• Tom: 89
• Numer: 3
• Strony: 203-246

Daty

wydano

2006

Twórcy

autor

Martintxo Saralegi-Aranguren

• Laboratoire de Mathématiques de Lens EA 2462, Fédération CNRS Nord-Pas-de-Calais FR 2956, Faculté des Sciences Jean Perrin, Université d'Artois, Rue Jean Souvraz S.P. 18, 62 307 Lens Cedex, France

autor

Robert Wolak

• Institute of Mathematics, Jagiellonian University, Reymonta 4, 30-059 Kraków, Poland

Identyfikatory

DOI

10.4064/ap89-3-1