K-homology and K-theory of pure braid groups

作者：Azzali, Sara^*; Browne, Sarah L.; Aparicio, Maria Paula Gomez; Ruth, Lauren C.; Wang, Hang

来源：New York Journal of Mathematics, 2022, 28: 1256-1294.

• pure braid
• K -theory
• K -homology
• Baum-Connes conjecture

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 [24]. We also discuss the case of the full braid group on 3-strands.

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