Restricted configuration spaces

TL;DR

This paper studies special subsets of configuration spaces in the complex plane, analyzing their fundamental groups and revealing new topological structures by removing finitely many hypersurfaces.

Contribution

It introduces a new class of restricted configuration spaces and computes their fundamental groups in low dimensions, expanding understanding of their topological properties.

Findings

Fundamental groups of restricted configuration spaces are explicitly computed in small dimensions.

Removing finitely many hypersurfaces creates fibrations over lower-dimensional configuration spaces.

New topological structures are identified in the restricted configuration spaces.

Abstract

Finitely many hypersurfaces are removed from unordered configuration spaces of $n$ points in $\mathbb{C}$ to obtain a fibration over unordered configuration spaces of $n-1$ complex points. Fundamental groups of these restricted configuration spaces are computed in small dimensions.