The moduli space of solutions to the Extended Bogomolny equations on $\Sigma \times \mathbb{R_+}$

Panagiotis Dimakis

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arXiv · 2401.10999

The moduli space of solutions to the Extended Bogomolny equations on $\Sigma \times \mathbb{R_+}$

Panagiotis Dimakis

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Abstract

We study moduli spaces of solutions to the extended Bogomolny equations on $\Sigma \times \mathbb{R_{+,y}}$ with gauge group $\operatorname{SL}(2,\mathbb{C})$ satisfying the generalized Nahm pole boundary condition as $y\to 0$ and limiting to complex flat connections as $y\to \infty$. Refining the Kobayashi-Hitchin correspondence of \cite{MH2}, we identify these moduli spaces with certain holomorphic lagrangian sub-manifolds inside the moduli space of Higgs bundles.

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Panagiotis Dimakis. 2024-01-19. The moduli space of solutions to the Extended Bogomolny equations on $\Sigma \times \mathbb{R_+}$. https://arxiv.org/abs/2401.10999

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