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 $S^1\times\Sigma\times R^+$

Siqi He, Stony Brook University
Fine Hall 314
We will discuss Witten’s gauge theory approach to Jones polynomial by counting solutions to the KapustinWitten(KW) equations with singular boundary conditions over 4manifolds. 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 HermitianYangMills type structure of KW monopole equation. This is based on joint works with Rafe Mazzeo.