| Title: |
Twisted local wild mapping class groups: configuration spaces, fission trees and complex braids |
| Authors: |
Boalch, Philip; Douçot, Jean; Rembado, Gabriele |
| Contributors: |
Institut de Mathématiques de Jussieu - Paris Rive Gauche (IMJ-PRG (UMR_7586)); Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité); Universidade de Lisboa = University of Lisbon = Université de Lisbonne Lisboa (ULISBOA); Institut Montpelliérain Alexander Grothendieck (IMAG); Centre National de la Recherche Scientifique (CNRS)-Université de Montpellier (UM); European Project |
| Source: |
ISSN: 0034-5318. |
| Publisher Information: |
CCSD; European Mathematical Society |
| Publication Year: |
2025 |
| Collection: |
Université de Montpellier: HAL |
| Subject Terms: |
mathematics of holonomic quantum fields; moduli spaces; nonlinear geometric local systems; wild Riemann surfaces; generalised braid groups; [MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG]; [MATH.MATH-GT]Mathematics [math]/Geometric Topology [math.GT]; [NLIN.NLIN-SI]Nonlinear Sciences [physics]/Exactly Solvable and Integrable Systems [nlin.SI] |
| Description: |
International audience ; 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. |
| Document Type: |
article in journal/newspaper |
| Language: |
English |
| DOI: |
10.4171/PRIMS/61-3-4 |
| Availability: |
https://hal.science/hal-03788461; https://hal.science/hal-03788461v5/document; https://hal.science/hal-03788461v5/file/twmcg.v6.pdf; https://doi.org/10.4171/PRIMS/61-3-4 |
| Rights: |
info:eu-repo/semantics/OpenAccess |
| Accession Number: |
edsbas.DF9AF253 |
| Database: |
BASE |