## Geometry and braiding of Stokes data; fission and wild character varieties.(English)Zbl 1283.53075

This paper constructs new algebraic Poisson varieties which generalize the complex varieties of Riemann surfaces. The author starts with the background definitions and properties. The spaces of Stokes data are introduced. The author proves that the space of Stokes data attached to a global irregular curve is an algebraic Poisson variety. Finally, it is shown that the family of Poisson varieties corresponding to admissible irregular curves fit together into a Poisson local system. The usual Poisson mapping class group actions on the character varieties are also generalized.

### MSC:

 53D17 Poisson manifolds; Poisson groupoids and algebroids 53D18 Generalized geometries (à la Hitchin)
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### References:

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