Geodesic
The $L^2$-Torsion Polytope of Amenable Groups
Documenta mathematica, Tome 23 (2018), pp. 1969-1993
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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 L2-torsion polytope among G-CW-complexes for these groups. As another application we prove that the L2-torsion polytope of an amenable group vanishes provided that it contains a non-abelian elementary amenable normal subgroup.
DOI : 10.4171/dm/665
Classification : 16S85, 20F65, 57Q10
Mots-clés : Atiyah conjecture, L2-torsion polytope, amenable groups, polytope class, 3-manifolds 
@article{10_4171_dm_665,
     author = {Florian Funke},
     title = {The $L^2${-Torsion} {Polytope} of {Amenable} {Groups}},
     journal = {Documenta mathematica},
     pages = {1969--1993},
     year = {2018},
     volume = {23},
     doi = {10.4171/dm/665},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/665/}
}
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Florian Funke. The $L^2$-Torsion Polytope of Amenable Groups. Documenta mathematica, Tome 23 (2018), pp. 1969-1993. doi: 10.4171/dm/665

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