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arXiv · 1704.07164

The $L^2$-torsion polytope of amenable groups

Florian Funke
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Abstract

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.

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Florian Funke. 2017-04-24. The $L^2$-torsion polytope of amenable groups. https://arxiv.org/abs/1704.07164

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