Topology of Galois conjugate character varieties

Junliang Shen; Siqing Zhang

Topology of Galois conjugate character varieties

Algebraic Geometry 2026-07-13 v1

Authors: Junliang Shen , Siqing Zhang

Abstract

We study the interaction between integral structures, automorphisms, and tautological relations for the cohomology of character varieties. Based on this, we propose a method to detect differences in the homotopy types of Galois conjugate character varieties. As an application, we find the first example of a pair of Galois conjugate character varieties that are not homotopy equivalent, answering negatively a 2005 question of Hausel.

Keywords

character varieties Galois conjugates homotopy types integral structures tautological relations cohomology

Cite

@article{arxiv.2607.12154,
  title  = {Topology of Galois conjugate character varieties},
  author = {Junliang Shen and Siqing Zhang},
  journal= {arXiv preprint arXiv:2607.12154},
  year   = {2026}
}