On the domain of the assembly map in algebraic k-theory

By Arthur Bartels. 2003

63 citations recorded by the source corpus.

We compare the domain of the assembly map in algebraic K { theory with respect to the family of nite subgroups with the domain of the assembly map with respect to the family of virtually cyclic subgroups and prove that the former is a direct summand of the later. AMS Classication 19D50; 19A31, 19B28

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/6dad2f1df06df52db3ff0682948d9708dea9800d

How researchers see this paper

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

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

The K-theoretic Farrell–Jones conjecture for hyperbolic groups (2007, background): “where Hn(BG;KR) is the homology theory associated to the (non-connective) K-theory spectrum KR of R evaluated at the classifying space BG of G, (C) runs through the conjugacy classes of maximal infinite cyclic subgroups of G and NKn(R) denotes the nth Bass-Nil-group of R. This follows from [ 9, Theo”
Isomorphism Conjecture for homotopy K-theory and groups acting on trees (2004, background): “In general, it is known [1] that the domain of the assembly map (0.”
On the classifying space of the family of virtually cyclic subgroups (2007, background): “Bartels [2] has shown that for every group G, every ring R, and every n ∈ Z the relative assembly map H n (EG;KR) → H G n (EG;KR) is split-injective.”
The Baum-Connes and the Farrell-Jones Conjectures in K- and L-Theory (2004, unknown): “Something similar remains true in general [16].”
On the Farrell–Jones Conjecture and its applications (2007, background): “(ii) For every group G, every ring R, and every n∈Z, the relative assembly map H n (EF in (G);KR ) → H n (EVCyc(G);KR ) is split-injective [9].”