K-homology and K-theory of pure Braid groups

2021/05/17 by Sara Azzali, Azzali, Sara, Sarah L. Browne +7 · 1 citation
Mathematics · #19D55 #20F36 #46L80 #58B34 #Advanced Operator Algebra Research #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.2105.07848

openalex publication_date 2021/05/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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. We also discuss the case of the full braid group B₃.

Citations

• The Baum-Connes conjecture and proper group actions on affine buildings

Cited by

• Remark on ordered braid groups

Related

• Homomorphisms between braid groups
• On braids and groups G_n^k
• Braid Groups are Linear
• Categorified invariants and the braid group
• Introduction to representations of braid groups