Tags: ? Refs: ? Links: de Rham moduli
Betti moduli
Betti moduli
- files without tags
-
character variety
\({\mathcal{M}}(\pi_1 \Sigma_g, \operatorname{GL}_n({\mathbf{C}})) = {\mathcal{M}}^{\operatorname{Betti}}_{g, n}\) is a Betti moduli space appearing the in nonabelian Hodge correspondence. Concretely, \begin{align*}{\mathcal{M}}_{g, n}^{\operatorname{Betti}}= \left\{{ \left\{{A_i, B_i}\right\}_{1\leq i \leq g} {~\mathrel{\Big\vert}~}\prod_{1\leq i \leq g}[A_i, B_i] = \operatorname{id}}\right\}/\operatorname{GL}_n({\mathbf{C}}),\end{align*} the moduli stack of representations of \(\pi_1 \Sigma_G\).