A new class of affine $K(\pi,1)$ arrangements

TL;DR

This paper introduces a new class of affine hyperplane arrangements that are proven to be $K(cpi,1)$ spaces by using an injective metric on Falk complexes, expanding the known examples in higher dimensions.

Contribution

It presents a novel method to establish the $K(cpi,1)$ property for affine arrangements using metric techniques on Falk complexes.

Findings

Identifies a new class of affine $K(cpi,1)$ arrangements.

Provides explicit constructions in dimensions greater than 2.

Expands the catalog of known infinite $K(cpi,1)$ arrangements.

Abstract

We show that a certain class of affine hyperplane arrangements are $K(\pi,1)$ by endowing their Falk complexes with an injective metric. This gives new examples of infinite $K(\pi,1)$ arrangements in dimension $n>2$.