The Groups $G_{n}^{k}$ and Fundamental Groups of Configuration Spaces
Vassily Olegovich Manturov

TL;DR
This paper explores the relationship between fundamental groups of plane configuration complements and the algebraic groups $G_{n}^{k}$, providing new insights into their connections and geometric realizations.
Contribution
It introduces a map linking fundamental groups to $G_{n}^{k}$ groups and discusses their interrelations and geometric interpretations.
Findings
Established a map from fundamental groups to $G_{n}^{k}$ groups.
Analyzed connections between different $G_{n}^{k}$ groups.
Explored geometric realizations of these groups.
Abstract
We construct a map from fundamental groups of complements to some plane configurations to the groups for large . We discuss connection between the groups for different and their geometric realization.
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Taxonomy
TopicsFinite Group Theory Research · Geometric and Algebraic Topology · Advanced Algebra and Geometry
