Algebraic K-theory over the infinite dihedral group: an algebraic approach
Davis, James F.
We prove that the Waldhausen nilpotent class group of an injective index 2 amalgamated free product is isomorphic to the Farrell-Bass nilpotent class group of a twisted polynomial extension. As an application, we show that the Farrell-Jones Conjecture in algebraic K-theory can be sharpened from the family of virtually cyclic subgroups to the family of finite-by-cyclic subgroups.
Mathematics - K-Theory and Homology, Mathematics - Algebraic Topology, 19D35 (Primary) 57Q10, 16E20 (Secondary)