2022/04/18 by Jean Douçot, Douçot, Jean, Gabriele Rembado +3 · 1 citation
Mathematics · #14D22 #14F35 #17B22 #32S22 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.2204.08188
openalex publication_date 2022/04/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We will define and study some generalisations of pure \mathfrakg-braid groups that occur in the theory of connections on curves, for any complex reductive Lie algebra \mathfrakg. They make up local pieces of the wild mapping class groups, which are fundamental groups of (universal) deformations of wild Riemann surfaces, underlying the braiding of Stokes data and generalising the usual mapping class groups. We will establish a general product decomposition for the local wild mapping class groups, and in many cases define a fission tree controlling this decomposition. Further in type A we will show one obtains cabled versions of braid groups, related to braid operads.