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arXiv · 1808.03886

The Expansions of the Nahm Pole Solutions to the Kapustin-Witten Equations

Siqi He
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Abstract

For a 3-manifold $X$ and compact simple Lie group $G$, we study the expansions of polyhomogeneous Nahm pole solutions to the Kapustin-Witten equations over $X\times (0,+\infty)$. Let $y$ be the coordinate of $(0,+\infty)$, we prove that the sub-leading terms of a polyhomogeneous Nahm pole solution is smooth to the boundary when $y\to 0$ if and only if $X$ is an Einstein 3-manifold.

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Siqi He. 2018-08-12. The Expansions of the Nahm Pole Solutions to the Kapustin-Witten Equations. https://arxiv.org/abs/1808.03886

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