Results in Mathematics

, Volume 54, Issue 1, pp 75-84

First online:

Basic Signature and Applications

  • Fouzi HathoutAffiliated withSaida university Email author 
  • , Mustapha DjaaAffiliated withSaida university

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

Mathematics Subject Classification (2000).

Primary 57R30 Secondary 14F40


Riemannian foliation basic cohomology basic signature