Betti numbers of the moduli space of Higgs bundles over a real curve

Thomas John Baird

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arXiv · 2512.06527

Betti numbers of the moduli space of Higgs bundles over a real curve

Thomas John Baird

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Abstract

We produce a formula for the $\mathbb{Z}_2$-Betti numbers of the moduli space $M_r^d$ of stable real Higgs bundles over a real projective curve, with coprime rank $r$ and degree $d$. Our approach relies on the motivic formula for the moduli space due to Mellit, Fedorov-Soibelman-Soibelman, and Schiffmann , and the fact that the virtual $\mathbb{Z}_2$ Poincar\'e polynomial is a motivic measure over $\mathbb{R}$.

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Thomas John Baird. 2025-12-06. Betti numbers of the moduli space of Higgs bundles over a real curve. https://arxiv.org/abs/2512.06527

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