Groups, Geometry, and Dynamics


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Volume 9, Issue 3, 2015, pp. 783–792
DOI: 10.4171/GGD/327

Published online: 2015-10-29

The Farrell–Jones conjecture for fundamental groups of graphs of abelian groups

Giovanni Gandini[1], Sebastian Meinert[2] and Henrik Rüping[3]

(1) Københavns Universitet, Copenhagen, Denmark
(2) Freie Universität Berlin, Germany
(3) The University of British Columbia, Vancouver, Canada

We show that the Farrell–Jones conjecture holds for fundamental groups of graphs of groups with abelian vertex groups. As a special case, this shows that the conjecture holds for generalized Baumslag–Solitar groups.

Keywords: Farrell–Jones Conjecture, algebraic K- and L-theory of group rings, fundamental groups of graphs of abelian groups, generalized Baumslag–Solitar groups, Baumslag– Solitar groups

Gandini Giovanni, Meinert Sebastian, Rüping Henrik: The Farrell–Jones conjecture for fundamental groups of graphs of abelian groups. Groups Geom. Dyn. 9 (2015), 783-792. doi: 10.4171/GGD/327