, Volume 54, Issue 1-2, pp 75-84

Basic Signature and Applications

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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 ${\mathcal{F}}_2$ .

Received: February 7, 2008. Revised: August 4, 2008. Accepted: November 10, 2008.