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Burghelea conjecture and asymptotic dimension of groups

Engel, Alexander ; Marcinkowski, Michał


We review the Burghelea conjecture, which constitutes a full computation of the periodic cyclic homology of complex group rings, and its relation to the algebraic Baum-Connes conjecture. The Burghelea conjecture implies the Bass conjecture. We state two conjectures about groups of finite asymptotic dimension, which together imply the Burghelea conjecture for such groups. We prove both conjectures ...


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