, Volume 54, Issue 1-2, pp 75-84
Date: 21 Jul 2009

Basic Signature and Applications

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Let M be a compact oriented manifold endowed with two orthogonal Riemannian foliations \({\mathcal{F}}_1\) and \({\mathcal{F}}_2\) respectively of codimensions \(n_1 = 4\ell_1\) and \(n_2 = 4\ell_2\). We prove that the signature Sing(M) of M is equal to \(Sing({\mathcal{F}}_1) · Sing({\mathcal{F}}_2)\) where \(Sing({\mathcal{F}}_1)\) and \(Sing({\mathcal{F}}_2)\) are the basic signatures respectively of the foliations \({\mathcal{F}}_1\) and \({\mathcal{F}}_2\).