It is conjectured that the coefficients of the Jones polynomial can be computed by counting solutions of the KW equations on a four-dimensional half-space, with certain boundary conditions that depend on a knot. The boundary conditions are defined by a "Nahm pole" away from the knot with a further singularity along the knot. In a previous paper, we gave a precise formulation of the Nahm pole boundary condition in the absence of knots, in the present paper, we do this in the more general case with knots included. We show that the KW equations with generalized Nahm pole boundary conditions are elliptic, and that the solutions are polyhomogeneous near the boundary and near the knot, with exponents determined by solutions of appropriate indicial equations. This involves the analysis of a "depth two incomplete iterated edge operator." As in our previous paper, a key ingredient in the analysis is a convenient new Weitzenb\"ock formula that is well-adapted to the specific problem.}

中文翻译：

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KW 方程和带结的 Nahm 极点边界条件

据推测，琼斯多项式的系数可以通过对四维半空间上的 KW 方程的解进行计数来计算，具有某些依赖于节点的边界条件。边界条件由远离节点的“Nahm 极点”定义，并且沿节点具有进一步的奇点。在之前的一篇论文中，我们给出了在没有结的情况下 Nahm 极点边界条件的精确公式，在本文中，我们在包含结的更一般情况下这样做。我们表明具有广义 Nahm 极点边界条件的 KW 方程是椭圆的，并且解在边界附近和节点附近是多齐次的，其指数由适当的指示方程的解确定。这涉及对“深度二不完全迭代边缘算子”的分析。