Inga Blomer
Towards the Atiyah Conjecture for Link Groups and their Extensions
Preprint series: Mathematica Gottingensis
MSC:
20E18
55N99
Abstract: A strong version of the Atiyah Conjecture for a group $G$ over the group ring $KG$ implies the Zero Divisor Conjecture for $G$ if $G$ is torsion free. Linnell and Schick have defined the class $\mathcal{F}$ of groups, which has the characteristic property that the strong Atiyah Conjecture is inherited by extensions with finite or elementary amenable quotient. We show that primitive Link Groups lie in $\mathcal{F}$ and investigate the requirements for a group to lie in $\mathcal{F}$ in detail. The importance of mild groups in this context is another major result.
Keywords: Atiyah Conjecture, Zero Divisor Conjecture, Primitive Link Groups, Mild Groups