Pseudogroup

Summary

A pseudogroup on a topological space is a collection of homeomorphisms between open subsets that is closed under composition, inversion, restriction and gluing. It records the local symmetries of a space, which need not extend to global ones. Pseudogroups are the transition rules of geometric structures: a smooth, complex or symplectic manifold is a space glued together by maps from the corresponding pseudogroup. They also describe the transverse structure of foliations.