THE L2-TORSION POLYTOPE OF AMENABLE GROUPS

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.