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

Nils-Edvin Enkelmann; Wolfgang Lück; Malte Pieper; Mark Ullmann; Christoph Winges

doi:10.2140/gt.2018.22.3321

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arXiv · 1607.06395

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

Nils-Edvin Enkelmann·Wolfgang Lück·Malte Pieper·Mark Ullmann·Christoph Winges

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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.

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Nils-Edvin Enkelmann, Wolfgang Lück, Malte Pieper, Mark Ullmann, Christoph Winges. 2016-07-21. On the Farrell-Jones Conjecture for Waldhausen's $A$-theory. https://doi.org/10.2140/gt.2018.22.3321

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