Modified Differentials and Basic Cohomology for Riemannian Foliations

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Date: July 2013
From: Journal of Geometric Analysis(Vol. 23, Issue 3)
Publisher: Springer
Document Type: Report
Length: 133 words

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Abstract :

Byline: Georges Habib (1), Ken Richardson (2) Keywords: Riemannian foliation; Basic Laplacian; Transverse geometry; Eigenvalue estimate; Basic cohomology; Poincare duality; 53C12; 53C21; 58J50; 58J60 Abstract: We define a new version of the exterior derivative on the basic forms of a Riemannian foliation to obtain a new form of basic cohomology that satisfies Poincare duality in the transversally orientable case. We use this twisted basic cohomology to show relationships between curvature, tautness, and vanishing of the basic Euler characteristic and basic signature. Author Affiliation: (1) Faculty of Sciences II, Department of Mathematics, Lebanese University, P.O. Box 90656, Fanar-Matn, Lebanon (2) Department of Mathematics, Texas Christian University, Fort Worth, TX, 76129, USA Article History: Registration Date: 30/11/2011 Received Date: 05/06/2011 Online Date: 20/12/2011 Article note: Communicated by Jiaping Wang. To the memory of Amine Fawaz.

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Gale Document Number: GALE|A337030648