English

Finite braid group orbits in Aff(C)-character varieties of the punctured sphere

Geometric Topology 2016-11-03 v2 Complex Variables Group Theory

Abstract

We give a complete description of finite braid group orbits in Aff(C)-character varieties of the punctured Riemann sphere. This is performed thanks to a coalescence procedure and to the theory of finite complex reflection groups. We then derive consequences in the theory of differential equations. These concern algebraicity of isomonodromic deformations for reducible rank two logarithmic connections on the sphere, the Riemann-Hilbert problem and F_D-type Lauricella hypergeometric functions.

Keywords

Cite

@article{arxiv.1604.04234,
  title  = {Finite braid group orbits in Aff(C)-character varieties of the punctured sphere},
  author = {Gaël Cousin and Delphine Moussard},
  journal= {arXiv preprint arXiv:1604.04234},
  year   = {2016}
}

Comments

To appear in International Math. Research Notices. No significant changes from the first version. 48 pages