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On
the Farrell–Jones conjecture for Waldhausen's $A$–theory
Nils-Edvin Enkelmann, Wolfgang Lück, Malte Pieper, Mark Ullmann and Christoph Winges |
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Geometry & Topology 22 (2018) 3321–3394
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Abstract |
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We prove the Farrell–Jones conjecture for (nonconnective) –theory with coefficients and finite wreath products for hyperbolic groups, –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. |
Keywords
Farrell–Jones conjecture, aspherical closed manifolds,
$A$–theory, Whitehead spaces, spaces of stable
pseudoisotopies, spaces of stable $h$–cobordisms
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Mathematical Subject Classification 2010
Primary: 19D10
Secondary: 57Q10, 57Q60
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References |
Publication
Received: 26 November 2016
Accepted: 4 March 2018
Published: 23 September 2018
Proposed: Steve Ferry
Seconded: Martin Bridson, Benson Farb
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Authors |
| Nils-Edvin Enkelmann | |
| Mathematisches Institut Rheinische Wilhelms-Universität Bonn Bonn Germany |
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| https://www.hcm.uni-bonn.de/people/profile/nils-edvin-enkelmann/ | |
| Wolfgang Lück | |
| Mathematisches Institut Rheinische Wilhelms-Universität Bonn Bonn Germany |
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| https://www.him.uni-bonn.de/lueck/ | |
| Malte Pieper | |
| Mathematisches Institut Rheinische Wilhelms-Universität Bonn Bonn Germany |
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| https://www.hcm.uni-bonn.de/people/profile/malte-pieper/ | |
| Mark Ullmann | |
| Institut für Mathematik FU Berlin Berlin Germany |
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| Christoph Winges | |
| Max-Planck-Institut für
Mathematik Bonn Germany |
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| http://people.mpim-bonn.mpg.de/winges/ | |
