Every graph \(\Gamma\) with edges labeled by elements of ℕ encodes an Artin group, which has generating set equal to the \(V(\Gamma)\) and relators \(aba... = bab...\) where both words are alternating and have length \(m_{a,b}\), the label on the edge between \(a\) and \(b\). Many basic questions about Artin groups remain open, including whether they are all torsion free, whether they are all CAT(0), whether they all have solvable word problem, and more. In this talk we address the Center Conjecture, which says that if an Artin group is irreducible and not of spherical type, then it has trivial center. We show that the center of any Artin group must be generated by cone points in its defining graph, and that if the subgroup generated by these points satisfies the center conjecture then so does the full group.
Centers of Artin Groups Defined on Cones
28.05.2024 15:00 - 17:00
Organiser:
G. Arzhantseva, Ch. Cashen
Location: