On the Farrell-Jones Conjecture for Waldhausen's $A$-theory

Abstract

We prove the Farrell-Jones Conjecture for (non-connective) $A$-theory with coefficients and finite wreath products for hyperbolic groups, CAT(0)-groups, cocompact lattices in almost connected Lie groups and fundamental groups of manifolds of dimension less or equal to three. Moreover, we prove inheritance properties such as passing to subgroups, colimits of direct systems of groups, finite direct products and finite free products. These results hold also for Whitehead spectra and spectra of stable pseudo-isotopies in the topological, piecewise linear and smooth category.

49 pages; improved exposition

References in corpus (3)

• The K-theoretic Farrell-Jones Conjecture for hyperbolic groups
• Splitting the relative assembly map, Nil-terms and involutions
• The A-theoretic Farrell-Jones Conjecture for virtually solvable groups

Cited by in corpus (5)

• Some finiteness results for groups of automorphisms of manifolds
• A vanishing theorem for tautological classes of aspherical manifolds
• Split injectivity of A-theoretic assembly maps
• On the Farrell-Jones Conjecture for algebraic K-theory of spaces: the Farrell-Hsiang method
• Riemannian foliation with exotic tori as leaves