Groups of type FP_2 over fields but not over the integers

Abstract: Being of type $\mathop{FP}_2$ is an algebraic shadow of being finitely presented. A long standing question was whether these two classes are equivalent. This was shown to be false in the work of Bestvina and Brady. More recently, there are many new examples of groups of type $\mathop{FP}_2$ coming with various interesting properties. I will begin with an introduction to the finiteness property $\mathop{FP}_2$. I will end by giving a construction to find groups that are of type $\mathop{FP}_2(F)$ for all fields $F$ but not $\mathop{FP}_2(\mathbb{Z})$

group theory

Audience: researchers in the discipline

Symmetry in Newcastle