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On the Farrell-Jones conjecture for Waldhausen’s \(A\)-theory. (English) Zbl 1453.19002

Summary: We prove the Farrell-Jones conjecture for (nonconnective) \(A\)-theory with coefficients and finite wreath products for hyperbolic groups, \(\operatorname{CAT}(0)\)-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 pseudoisotopies in the topological, piecewise linear and smooth categories.

MSC:

19D10 Algebraic \(K\)-theory of spaces
57Q10 Simple homotopy type, Whitehead torsion, Reidemeister-Franz torsion, etc.
57Q60 Cobordism and concordance in PL-topology
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