Equivariant covers for hyperbolic groups
By Arthur Bartels, W. Lück, H. Reich. 2006
51 citations recorded by the source corpus.
Recall that a cover U is of dimension N if every x 2 X is contained in no more then N C 1 members of U . The asymptotic dimension of a finitely generated group is its asymptotic dimension as a metric space with respect to any word metric. An important result of Yu [19] asserts that the Novikov conjecture holds for groups of finite asymptotic dimension. This can be viewed as an injectivity result for the assembly map in L–theory (after inverting 2). Further injectivity results for assembly maps for groups with finite asymptotic dimension can be found in Bartels [1], Carlsson and Goldfarb [6] and Bartels and Rosenthal [4]. On the other hand no surjectivity statement of assembly maps is known for all groups of finite asymptotic dimension and this is very much related to the absence of any equivariance condition for the cover U as above.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/2b7c0d3230a34147399c48a18c12904d1cc8c321
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In Geometry and Topology
- G'abor Szab'o
- J. Zacharias
- W. Lück
- Arthur Bartels
- Guoliang Yu
- Rufus Willett
- Ilan Hirshberg
- Jianchao Wu
In Mathematical Physics
- G'abor Szab'o
- Rufus Willett
- W. Winter
- J. Zacharias
- Guoliang Yu
- Ilan Hirshberg
- Jianchao Wu
- Arthur Bartels
Citations in the corpus
- 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.”
- Rokhlin Dimension and C*-Dynamics (2012, methodology): “Finally, we mention that Bartels, Lück and Reich have studied a concept closely related to ours in [2]; this idea plays a key role in their proof of the Farrell-Jones conjecture for hyperbolic groups in [3].”
- The Borel Conjecture for hyperbolic and CAT(0)-groups (2009, methodology): “This will essentially follow from [7] and [13] , see also [8, Lemma 2.”
- Rokhlin dimension for actions of residually finite groups (2014, methodology): “We remark that before this work, a similar concept had been defined, at least implicitly, in the pioneering work [4] of Bartels, Lück and Reich on the Farrell–Jones conjecture for hyperbolic groups.”