Work

Local wild mapping class groups and cabled braids

Year: 2026

Type: article

Abstract: We define and study some generalisations of pure 𝔤 -braid groups, for any complex reductive Lie algebra 𝔤 . They naturally occur in the theory of isomonodromic deformations for meromorphic connections with irregular singularities on principal bundles over Riemann surfaces, covering the general untwisted case, going beyond the case of generic irregular types. These generalised braid groups make up local pieces of the wild mapping class groups, which in turn extend the usual mapping class groups and govern the braiding of Stokes data. We establish a general product decomposition for these local wild mapping class groups, and in all classical cases define a fission tree governing the decomposition; in particular in type D we will find a factor which is not isomorphic to any pure braid group coming from a root system. In type A , the fission tree and the pure braid group operad yields a proof of the corresponding “multi-scale” braiding conjecture.

Source: Annales de l’institut Fourier

DOI: 10.5802/aif.3778

Authors: Jean Douçot, Gabriele Rembado, Matteo Tamiozzo

Institutions: University of Lisbon, University of Bonn, Hausdorff Center for Mathematics, University of Warwick

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: European Commission, Deutsche Forschungsgemeinschaft

Awards: EXC 2047: Hausdorff Center for Mathematics (HCM), G8847963564