# Basic Signature and Applications

## Authors

- First Online:

DOI: 10.1007/s00025-009-0368-y

- Cite this article as:
- Hathout, F. & Djaa, M. Results. Math. (2009) 54: 75. doi:10.1007/s00025-009-0368-y

- 1 Citations
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## 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 \({\mathcal{F}}_2\).