K-homology and K-theory of pure Braid groups

Abstract

We produce an explicit description of the K-theory and K-homology of the pure braid group on n strands. We describe the Baum-Connes correspondence between the generators of the left-and right-hand sides for n = 4. Using functoriality of the assembly map and direct computations, we recover Oyono-Oyono's result on the Baum-Connes conjecture for pure braid groups [OO01]. We also discuss the case of the full braid group B3.

Bredon homology of Artin groups of dihedral type

“…See [42] for a good survey. In this context, Azzali et al have recently computed explicitly both sides of Baum-Connes for pure braid groups [4]; in joint work of the second author with J. González-Meneses [21] it is computed the minimal dimension of a model of EG for braid groups; J. and virtually-cyclic dimensions of mapping class groups (which include in particular certain Artin groups) have been recently investigated by Aramayona et al ([1], [2]) and by Petrosyan and Nucinkis [40].…”