The Baum-Connes and the Farrell-Jones Conjectures in K- and L-Theory

By W. Lück, H. Reich. 2004

239 citations recorded by the source corpus.

We give a survey of the meaning, status and applications of the Baum-Connes Conjecture about the topological K-theory of the reduced group C^*-algebra and the Farrell-Jones Conjecture about the algebraic K- and L-theory of the group ring of a (discrete) group G.

Subfields: Algebra and Number Theory, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/57c38235a8d440eeba2e6a6b84dee33be8258b3c

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. W. Lück
2. Arthur Bartels
3. H. Reich
4. M. Kreck
5. Holger Kammeyer
6. Henrik Rueping
7. Christian Wegner

In Mathematical Physics

1. W. Lück
2. Arthur Bartels
3. H. Reich
4. Holger Kammeyer
5. Henrik Rueping
6. F. Thomas Farrell
7. Christian Wegner
8. M. Kreck

Citations in the corpus

• TOPOLOGICAL 4-MANIFOLDS WITH GEOMETRICALLY TWO-DIMENSIONAL FUNDAMENTAL GROUPS (2008, background): “We refer to [26] for a survey of results on these conjectures.”
• The K-theoretic Farrell–Jones conjecture for hyperbolic groups (2007, background): “For more explanations, information about the status and references concerning the Farrell-Jones Conjecture we refer to the survey article [46].”
• The Borel Conjecture for hyperbolic and CAT(0)-groups (2009, methodology): “See [42] for a survey on the Farrell-Jones Conjectures.”
• The Farrell-Jones Conjecture for cocompact lattices in virtually connected Lie groups (2011, background): “For a detailed discussion of these applications we refer to [10] and the survey article [30].”
• The Farrell–Jones conjecture for arbitrary lattices in virtually connected Lie groups (2014, background): “For an overview of the Farrell-Jones conjecture and its consequences, see for instance [5, 20, 21].”
• Isomorphism Conjecture for homotopy K-theory and groups acting on trees (2004, background): “For more information about the various conjectures such as the version for pseudoisotropy or the Baum–Connes Conjecture we refer for instance to [18].”
• On the Farrell–Jones Conjecture and its applications (2007, methodology): “In particular we get an equivariant homology theory with values in Z-modules in the sense above for algebraic K-theory (see [20, Section 2], [ 45, Theorem 6.1 ]).”
• Topological rigidity for non-aspherical manifolds (2005, methodology): “(We can ignore the decoration by the Rothenberg sequences and the assumption that Wh(G) and K̃n(ZG) vanish for n ≤ 0.)”