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Complex, contact, Riemannian, pseudo-Riemannian and Finsler geometry, relativity, gauge theory, global analysis.
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Is there a "geometric" language that describes the equivalence groupoid of a foliated manifold?
If your foliation is "regular", which roughly means the leaves have constant dimension, then every chart of the manifold has the form $L \times T$, where $L$ is the longitudinal (leafwise) direction a …