Twisted local wild mapping class groups: configuration spaces, fission trees and complex braids - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2024

Twisted local wild mapping class groups: configuration spaces, fission trees and complex braids

Résumé

Following the completion of the algebraic construction of the Poisson wild character varieties (B.–Yamakawa 2015) one can consider their natural deformations, generalising both the mapping class group actions on the usual (tame) character varieties, and the G-braid groups already known to occur in the wild/irregular setting. Here we study these wild mapping class groups in the case of arbitrary formal structure in type A. As we will recall, this story is most naturally phrased in terms of admissible deformations of wild Riemann surfaces. The main results are: 1) the construction of configuration spaces containing all possible local deformations, 2) the definition of a combinatorial object, the “fission forest”, of any wild Riemann surface and a proof that it gives a sharp parameterisation of all the admissible deformation classes. As an application of 1), by considering basic examples, we show that the braid groups of all the complex reflection groups known as the generalised symmetric groups appear as wild mapping class groups. As an application of 2), we compute the dimensions of all the (global) moduli spaces of type A wild Riemann surfaces (in fixed admissible deformation classes), a generalisation of the famous “Riemann’s count” of the dimensions of the moduli spaces of compact Riemann surfaces.
Fichier principal
Vignette du fichier
twmcg.pdf (294.53 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03788461 , version 1 (26-09-2022)
hal-03788461 , version 2 (24-11-2023)
hal-03788461 , version 3 (27-03-2024)

Identifiants

  • HAL Id : hal-03788461 , version 3

Citer

Philip Boalch, Jean Douçot, Gabriele Rembado. Twisted local wild mapping class groups: configuration spaces, fission trees and complex braids. 2024. ⟨hal-03788461v3⟩
62 Consultations
34 Téléchargements

Partager

Gmail Facebook X LinkedIn More