Geodesic
The $L^2$-Torsion Polytope of Amenable Groups
Documenta mathematica, Tome 23 (2018), pp. 1969-1993.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

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.
Classification : 20F65, 57Q10, 16S85
Keywords: $L^2$-torsion polytope, amenable groups, polytope class, Atiyah conjecture, $3$-manifolds 
@article{DOCMA_2018__23__a7,
     author = {Funke, Florian},
     title = {The $L^2${-Torsion} {Polytope} of {Amenable} {Groups}},
     journal = {Documenta mathematica},
     pages = {1969--1993},
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     volume = {23},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2018__23__a7/}
}
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Funke, Florian. The $L^2$-Torsion Polytope of Amenable Groups. Documenta mathematica, Tome 23 (2018), pp. 1969-1993. http://geodesic.mathdoc.fr/item/DOCMA_2018__23__a7/