# Topology of complements to real affine space line arrangements

## TL;DR

This paper proves that the topological type of the space remaining after removing a real affine line arrangement depends solely on the number of lines and their intersection data, regardless of the ambient space dimension.

## Contribution

It establishes that the diffeomorphism type of line arrangement complements is fully determined by simple combinatorial data, extending previous results to all dimensions.

## Key findings

- Diffeomorphism type depends only on line count and intersection data.
- Results apply to arrangements in any dimension.
- Simplifies classification of line arrangement complements.

## Abstract

It is shown that the diffeomorphism type of the complement to a real space line arrangement in any dimensional affine ambient space is determined only by the number of lines and the data on multiple points.