# The modular class of a singular foliation

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The modular class is a generalization of the divergence of vector fields to other geometric structures such as Poisson manifolds and Lie algebroids. The modular class of a regular foliation involves a volume form on the conormal bundle and the associated Bott connection. It is a closed one form along the leaves. The vanishing of this modular class implies that there exists a volume form which is invariant along the leaves. In the singular case, the above definition can not be summoned since the conormal bundle may not be even well defined.