Centers of Artin groups defined on cones

TL;DR

This paper proves that the Center Conjecture for Artin groups on cone graphs can be reduced to the conjecture on the cone points, confirming it for groups with a single cone point.

Contribution

It establishes a reduction of the Center Conjecture to simpler cases for Artin groups defined on cone graphs, expanding the classes where the conjecture holds.

Findings

Center Conjecture passes to cone Artin groups if it holds on cone points.

Confirmed the conjecture for Artin groups with exactly one cone point.

Provides a method to verify the conjecture for broader classes of Artin groups.

Abstract

We prove that the Center Conjecture passes to the Artin groups whose defining graphs are cones, if the conjecture holds for the Artin group defined on the set of the cone points. In particular, it holds for every Artin group whose defining graph has exactly one cone point.