The Borel Conjecture for hyperbolic and CAT(0)-groups

By Arthur Bartels, W. Lück. 2009

215 citations recorded by the source corpus.

We prove the Borel Conjecture for a class of groups containing word-hyperbolic groups and groups acting properly, isometrically and cocompactly on a finite dimensional CAT(0)-space.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/e0bcb566586701fd18dd0c56311bef04578f038e

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Citations in the corpus

The Farrell-Jones Conjecture for cocompact lattices in virtually connected Lie groups (2011, result): “Since every group G which acts cocompactly, isometrically and properly on a complete, simply connected Riemannian manifold with non-positive sectional curvature is a cocompact CAT(0)-group, it satisfies the FJC by the main results from [6, 39].”
A counterexample to the unit conjecture for group rings (2021, background): “The group P satisfies the Farrell–Jones conjecture (indeed, it is the fundamental group of the flat manifold of Hantzsche–Wendt so it is covered by the original work of Farrell–Jones [FJ93] for integral coefficients and by [BL12] for general coefficients) so one interpretation of Theorem A is that t”
A notion of geometric complexity and its application to topological rigidity (2010, unknown): “Many important results on the Borel conjecture have been obtained by Farrell and Jones [13– 16], and more recently Bartels and Lück [3].”
Dynamic asymptotic dimension: relation to dynamics, topology, coarse geometry, and $$C^*$$C∗-algebras (2015, background): “4 we discuss the connection to the work of Bartels, Lück, and Reich [1,3] in controlled topology.”
The "K"-theoretic Farrell-Jones conjecture for CAT(0)-groups (2010, methodology): “ecture with coeﬃcients forCAT(0)-groups. ByaCAT(0)-groupwemeanagroupwhichadmits acocompact proper action by isometries on a ﬁnite dimensional CAT(0)-space. The proof is based on methods from [BLR08], [BL09] and [BL10]. In [BLR08] Bartels, Lu¨ck and Reich show the bijectivity of the K-theoretic assem”
A metric Kan–Thurston theorem (2010, background): “e, where KH ∗ (∗) is isomorphic to Z[1/2]⊗L h−∞i ∗ (RH), the algebraic Lgroups of RH localized away from the prime 2. The Farrell-Jones conjecture in algebraic L-theory is proved for CAT(0) groups in [2], and hence Theorem 10.1 applies directly for this choice of K? ∗. – Let R be a regular ring, and”
The Farrell–Jones conjecture for virtually solvable groups (2013, methodology): “groups. 1 2 CHRISTIAN WEGNER (2) Transfer reducibility. This method using the geodesic ﬂow was pioneered by Farrell-Jones and later extended to hyperbolic groups (see [BLR08b]) and CAT(0)-groups (see [BL12a], [Weg12]). We call groups which satisfy the combined method Farrell-Hsiang-Jones groups (”FH”