Farrell-Jones conjecture for fundamental groups of graphs of virtually cyclic groups (Q281717)

The author proves that the \(K\)- and \(L\)-theoretic Farrell-Jones Conjecture with coefficients in an additive category and finite wreath products is true for fundamental groups of graphs of virtually cyclic groups. In particular, any HNN extension of virtually cyclic groups satisfy the Farrell-Jones Conjecture. The method of the proof is to map the group to some group that is known to satisfy the \(K\)- and \(L\)-theoretic Farrell-Jones Conjecture with finite wreath products and coefficients in an additive category (FJCw), and then use inheritance properties of FJCw. It also uses a very recent result of \textit{A.~Bartels} [``Coarse flow spaces for relatively hyperbolic groups'', preprint, \url{arXiv:1502.04834}] which says that FJCw is closed under taking amalgamated products and HNN extensions along a finite subgroup.