Hyperplane arrangements in negatively curved manifolds and relative hyperbolicity

TL;DR

This paper demonstrates that specific aspherical manifolds derived from hyperplane arrangements in negatively curved spaces have fundamental groups that are relatively hyperbolic, linking geometric structures to algebraic properties.

Contribution

It establishes a connection between hyperplane arrangements in negatively curved manifolds and the relative hyperbolicity of their fundamental groups, a novel geometric group theory result.

Findings

Certain aspherical manifolds have relatively hyperbolic fundamental groups.

Hyperplane arrangements influence the algebraic properties of the manifold's fundamental group.

The work bridges geometric configurations with group-theoretic hyperbolicity.

Abstract

We show that certain aspherical manifolds arising from hyperplane arrangements in negatively curved manifolds have relatively hyperbolic fundamental group.