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The Baum-Connes conjecture: an extended survey. (English) Zbl 1447.58006

Chamseddine, Ali (ed.) et al., Advances in noncommutative geometry. Based on the noncommutative geometry conference, Shanghai, China, March 23 – April 7, 2017. On the occasion of Alain Connes’ 70th Birthday. Cham: Springer. 127-244 (2019).
The Baum-Connes (BC) conjecture has been a great source of inspiration for developments in Noncommutative Geometry. The paper under view provides a comprehensive survey on the BC conjecture and related topics, including the BC conjecture with coefficients and the coarse BC conjecture. Starting with the history that led to the conjecture, it describes tools, techniques and methods that have been central for developments, while it gathers known results. The presentation is well-thought with plenty of comments, historical remarks and co-ordinates, and the paper can be quite helpful as an introduction to understand and pursue research in the subject.
For the entire collection see [Zbl 1432.58003].

MSC:

58B34 Noncommutative geometry (à la Connes)
46L05 General theory of \(C^*\)-algebras
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Full Text: DOI arXiv

References:

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