The \(L^2\)-torsion polytope of amenable groups (Q1756290)

Summary: We introduce the notion of groups of polytope class and show that torsion-free amenable groups satisfying the Atiyah Conjecture possess this property. A direct consequence is the homotopy invariance of the \(L^2\)-torsion polytope among \(G\)-CW-complexes for these groups. As another application we prove that the \(L^2\)-torsion polytope of an amenable group vanishes provided that it contains a non-abelian elementary amenable normal subgroup.