On the Isoperimetric functions of a class of Artin Groups

TL;DR

This paper establishes a polynomial isoperimetric function for a class of Artin groups with specific graph properties, demonstrating their word problem is solvable using small cancellation theory.

Contribution

It introduces a polynomial isoperimetric function for certain Artin groups, expanding understanding of their geometric and algorithmic properties.

Findings

Polynomial isoperimetric function of n^6 for these Artin groups

Proof that these Artin groups have solvable word problem

Application of small cancellation theory to analyze group properties

Abstract

We find a polynomial (n^6) isoperimetric function for Artin groups, the defining graph of which contains no edges labelled by 3. This in particular shows that even Artin groups have solvable word problem. We use small cancellation theory of relative extended presentations.