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arXiv · 2607.12154

Topology of Galois conjugate character varieties

Junliang Shen·Siqing Zhang
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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.

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Junliang Shen, Siqing Zhang. 2026-07-13. Topology of Galois conjugate character varieties. https://arxiv.org/abs/2607.12154

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