Minimal disc diagrams of 5/9-simplicial complexes

TL;DR

This paper introduces the 5/9-condition for simplicial complexes, demonstrating it implies Gromov hyperbolicity of their universal covers and providing new insights into combinatorial conditions like 8-location.

Contribution

It establishes the 5/9-condition as a new local combinatorial criterion ensuring hyperbolicity, and proves the minimal filling diagram lemma for these complexes.

Findings

5/9-condition implies Gromov hyperbolicity

Proves minimal filling diagram lemma for 5/9-complexes

Connects 8-location condition with hyperbolicity

Abstract

We introduce and study a local combinatorial condition, called the 5/9-condition, on a simplicial complex, implying Gromov hyperbolicity of its universal cover. We hereby give an application of another combinatorial condition, called 8-location, introduced by Damian Osajda. Along the way we prove the minimal filling diagram lemma for 5/9-complexes.