naa a22 4500 510810713 CHVBK 20180411083441.0 cr unu---uuuuu 180411e20130701xx s 000 0 eng 10.1007/s12220-011-9289-6 doi (NATIONALLICENCE)springer-10.1007/s12220-011-9289-6 Modified Differentials and Basic Cohomology for Riemannian Foliations [Elektronische Daten] [Georges Habib, Ken Richardson] 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 Poincaré 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. Mathematica Josephina, Inc., 2011 Riemannian foliation nationallicence Basic Laplacian nationallicence Transverse geometry nationallicence Eigenvalue estimate nationallicence Basic cohomology nationallicence Poincaré duality nationallicence Habib Georges Faculty of Sciences II, Department of Mathematics, Lebanese University, P.O. Box 90656, Fanar-Matn, Lebanon aut Richardson Ken Department of Mathematics, Texas Christian University, 76129, Fort Worth, TX, USA aut Journal of Geometric Analysis Springer US; http://www.springer-ny.com 23/3(2013-07-01), 1314-1342 1050-6926 23:3<1314 2013 23 12220 https://doi.org/10.1007/s12220-011-9289-6 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s12220-011-9289-6 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Habib Georges Faculty of Sciences II, Department of Mathematics, Lebanese University, P.O. Box 90656, Fanar-Matn, Lebanon aut NATIONALLICENCE 700 1- Richardson Ken Department of Mathematics, Texas Christian University, 76129, Fort Worth, TX, USA aut NATIONALLICENCE 773 0- Journal of Geometric Analysis Springer US; http://www.springer-ny.com 23/3(2013-07-01), 1314-1342 1050-6926 23:3<1314 2013 23 12220 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer