Classification of Nahm Pole Solutions to the KW Equations on $S^1\times\Sigma\times R^+$

Classification of Nahm Pole Solutions to the KW Equations on $S^1\times\Sigma\times R^+$

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Siqi He, Stony Brook University
Fine Hall 314

We will discuss Witten’s gauge theory approach to Jones polynomial by counting solutions to the Kapustin-Witten(KW) equations with singular boundary conditions over 4-manifolds. We will give a classification of solutions to the KW equations over $S^1\times\Sigma\times R^+$.

We prove that all solutions to the KW equations over $S^1\times\Sigma\times R^+$ are $S^1$ direction invariant and we give a classification of the KW monopole over $\Sigma\times R^+$ based on the Hermitian-Yang-Mills type structure of KW monopole equation. This is based on joint works with Rafe Mazzeo.