Algebraic K-theory over the infinite dihedral group: an algebraic approach

Abstract

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.

References in corpus (4)

• The K-theoretic Farrell-Jones Conjecture for hyperbolic groups
• Algebraic K-theory over the infinite dihedral group: a controlled topology approach
• Some remarks on Nil groups in algebraic K-theory
• Splitting formulas for certain Waldhausen Nil-groups

Cited by in corpus (7)

• Recollements of derived categories II: Algebraic K-theory
• Lower algebraic K-theory of certain reflection groups
• Topological rigidity and actions on contractible manifolds with discrete singular set
• On the algebraic $K$-theory of the Hilbert modular group
• Revisiting Farrell's nonfiniteness of Nil
• On the vanishing of the lower K-theory of the Holomorph of a free group on two generators
• On the algebraic K-theory of 3-manifold groups