Tbilisi Mathematical Journal

Homological algebra in bivariant K-theory and other triangulated categories. II

Ralf Meyer

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Abstract

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.

Note

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

Article information

Source
Tbilisi Math. J., Volume 1 (2008), 165-210.

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

Permanent link to this document
https://projecteuclid.org/euclid.tbilisi/1528768828

Digital Object Identifier
doi:10.32513/tbilisi/1528768828

Mathematical Reviews number (MathSciNet)
MR2563811

Zentralblatt MATH identifier
1161.18301

Subjects
Primary: 18E30: Derived categories, triangulated categories
Secondary: 19K35: Kasparov theory ($KK$-theory) [See also 58J22] 46L80: $K$-theory and operator algebras (including cyclic theory) [See also 18F25, 19Kxx, 46M20, 55Rxx, 58J22] 55U35: Abstract and axiomatic homotopy theory

Keywords
triangulated category Baum–Connes conjecture phantom map spectral sequence

Citation

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


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