Studying complex manifolds by using groups $G_n^k$ and $\Gamma_n^k$

In this talk, we study several complex manifolds by using the following idea. First, we construct a certain moduli space and study the fundamental group of this space. This fundamental group is naturally mapped to the groups $G_n^k$ and $\Gamma_n^k$. This is the step towards “complexification” of the $G_n^k$ and $\Gamma_n^k$ approach first developed in arXiv: 1905.08049. This is my joint work with Vassily O. Manturov (arXiv: 2001.02791).