Title: Finiteness properties and free Abelian groups

 

Abstract: Finiteness properties of groups come in many flavours, I will discuss topological finiteness properties. These relate to the finiteness of skelata in a classifying space. Groups with interesting finiteness properties have been found in many ways, however all such examples contains free Abelian subgroups of high rank. I will discuss some constructions of groups discussing the various ways we can reduce the rank of free Abelian subgroups. I will introduce all the concepts required for my talk.