Studying complex manifolds by using groups Gnk and Γnk

Abstract

In this paper, 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 [Formula: see text] and [Formula: see text]. This is the step towards “complexification” of the [Formula: see text] and [Formula: see text] approach first developed in [V. O. Manturov, D. A. Fedoseev, S. Kim and I. M. Nikonov, On groups [Formula: see text] and [Formula: see text]: A study of manifolds, dynamics, and invariants, preprint (2019), arXiv:1905.08049 ].