Definition
Irregular-singular connection
A meromorphic flat connection whose singularity is not regular singular and whose local classification requires exponential and Stokes data.
Definition
Let be a punctured smooth complex curve. A meromorphic flat connection on has an irregular singularity at if it is not regular singular there.
After a finite ramified cover and a formal gauge transformation, an irregular connection decomposes into pieces containing nonconstant exponential factors. These factors, together with formal monodromy, describe its formal type.
Analytic classification
Formal type does not determine the analytic connection. Sectorial fundamental solutions differ by Stokes data, which record the missing analytic information.
References
- Philip Boalch, “Geometry and braiding of Stokes data; fission and wild character varieties,” Annals of Mathematics 179 (2014), 301–365. arXiv.