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2008 Homological algebra in bivariant K-theory and other triangulated categories. II
Ralf Meyer
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Tbilisi Math. J. 1: 165-210 (2008). DOI: 10.32513/tbilisi/1528768828


We use homological ideals in triangulated categories to get a sufficient criterion for a pair of subcategories in a triangulated category to be complementary. We apply this criterion to construct the Baum-Connes assembly map for locally compact groups and torsion-free discrete quantum groups. Our methods are related to the abstract version of the Adams spectral sequence by Brinkmann and Christensen.

Funding Statement

Supported by the German Research Foundation (Deutsche Forschungsgemeinschaft (DFG)) through the Institutional Strategy of the University of Göttingen.


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Ralf Meyer. "Homological algebra in bivariant K-theory and other triangulated categories. II." Tbilisi Math. J. 1 165 - 210, 2008.


Received: 17 July 2008; Revised: 4 December 2008; Accepted: 15 December 2008; Published: 2008
First available in Project Euclid: 12 June 2018

zbMATH: 1161.18301
MathSciNet: MR2563811
Digital Object Identifier: 10.32513/tbilisi/1528768828

Primary: 18E30
Secondary: 19K35 , 46L80 , 55U35

Keywords: Baum–Connes conjecture , phantom map , spectral sequence , triangulated category

Rights: Copyright © 2008 Tbilisi Centre for Mathematical Sciences


Vol.1 • 2008
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