K-homology and K-theory of pure Braid groups
K-Theory and Homology
2022-08-17 v2 Operator Algebras
Abstract
We produce an explicit description of the K-theory and K-homology of the pure braid group on strands. We describe the Baum--Connes correspondence between the generators of the left- and right-hand sides for . 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 .
Cite
@article{arxiv.2105.07848,
title = {K-homology and K-theory of pure Braid groups},
author = {Sara Azzali and Sarah L. Browne and Maria Paula Gomez Aparicio and Lauren C. Ruth and Hang Wang},
journal= {arXiv preprint arXiv:2105.07848},
year = {2022}
}
Comments
39 pages, revised version to appear on New York J. Math