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Beschreibung:
This thesis contains three projects revolving around the L 2 -torsion polytope. First we show that the L 2 -torsion polytope of infinite elementary amenable groups vanishes. Then we establish a link between the L 2 -torsion polytope and the Bieri-Neumann-Strebel invariant for a particular class of free-by-cyclic groups. We finally investigate the integral polytope group as this is the place where the L 2 -torsion polytope takes values in.