Monodromy

Summary

Monodromy describes how a multivalued object changes when it is continued around a loop. Take a linear differential equation with singular points, and continue a basis of solutions around one of them. The result is a new basis, related to the old one by an invertible matrix. These matrices form a representation of the fundamental group of the plane minus the singular points, the monodromy representation. It is a global invariant of the equation, and it is the subject of Hilbert's twenty-first problem. See the definition and the related monodromy theorem.