Factor system for graphs and combinatorial HHS

TL;DR

This paper extends the combinatorial HHS framework to a broader class of graphs, specifically cubical curve graphs, and applies it to quasi-median graphs, broadening the scope of factor system machinery.

Contribution

It relaxes constraints on combinatorial HHS domains and extends factor system machinery from CAT(0) cube complexes to quasi-median graphs.

Findings

HHS machinery now applies to most cubical curve graphs.

Extended factor system machinery to quasi-median graphs.

Broadened applicability of combinatorial HHS methods.

Abstract

We relaxe the constraint on the domains of combinatorial HHS machinery so combinatorial HHS machinery works for most cubical curve graphs. As an application we extend the factor system machinery of the CAT(0) cube complex to the quasi-median graphs.