I’ve been trying to write down the construction for the Poisson structure of the knot character varieties, and it got me thinking about the Poisson geometry of the Grothendieck resolution and how it ties with our rank 1 and higher rank microlocal support conditions. Let’s consider two trivial cases of our knot character varieties. Consider …

Read more

Long time no post. Boalch proved in some of his papers that the wild character variety on the punctured $\mathbb A^1$ comes from a quasi-Hamiltonian reduction of a “higher fission space” $_G A_H$ by actions of $G$ and $H$ (some Levi subgroup in $G$). The quotient $_G A_H / (G \times H)$ thus carries a Poisson structure, …

Read more