1. K-homology and K-theory of pure Braid groups
- Author
-
Azzali, Sara, Browne, Sarah L., Aparicio, Maria Paula Gomez, Ruth, Lauren C., and Wang, Hang
- Subjects
Mathematics - K-Theory and Homology ,Mathematics - Operator Algebras ,58B34, 19D55, 46L80, 20F36 - 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 $B_3$., Comment: 39 pages, revised version to appear on New York J. Math
- Published
- 2021