Definition
Stokes data
The sectorial transition data that, together with formal type, classify an irregular meromorphic connection analytically.
Definition
Near an irregular singularity, choose sectorial fundamental solutions having a fixed formal asymptotic expansion. On overlaps of adjacent sectors, two such solutions differ by a locally constant unipotent transformation. The resulting transformations, indexed by the singular directions and subject to their product and compatibility relations, are the Stokes data of the connection.
Stokes data are invariant under changes of sectorial solutions up to the appropriate simultaneous gauge equivalence. Formal type, formal monodromy, and Stokes data together recover the local analytic isomorphism class; formal type and ordinary monodromy alone generally do not.
References
- Philip Boalch, “Geometry and braiding of Stokes data; fission and wild character varieties,” Annals of Mathematics 179 (2014), 301–365. arXiv.