Results in Mathematics

, Volume 54, Issue 1–2, pp 75–84 | Cite as

Basic Signature and Applications

Article

Abstract.

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 \({\mathcal{F}}_2\).

Mathematics Subject Classification (2000).

Primary 57R30 Secondary 14F40 

Keywords.

Riemannian foliation basic cohomology basic signature 

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2009

Authors and Affiliations

  1. 1.Saida universitySaidaAlgeria

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