Braid groups in complex spaces

TL;DR

This paper investigates the fundamental groups of configuration spaces of points in complex n-dimensional space, focusing on their algebraic structure and properties.

Contribution

It provides a detailed description of the fundamental groups of ordered and unordered point sets in complex spaces, highlighting their generating affine subspaces.

Findings

Characterization of fundamental groups of point configuration spaces

Identification of algebraic structures of these groups

Insights into the topology of complex configuration spaces

Abstract

We describe the fundamental groups of ordered and unordered $k-$point sets in the n-dimensional complex space $C^n$ generating an affine subspace of fixed dimension.