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arXiv · 2105.07848

K-homology and K-theory of pure Braid groups

Sara Azzali·Sarah L. Browne·Maria Paula Gomez Aparicio·Lauren C. Ruth·Hang Wang
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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 $B_3$.

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Sara Azzali, Sarah L. Browne, Maria Paula Gomez Aparicio, Lauren C. Ruth, Hang Wang. 2022-08-16. K-homology and K-theory of pure Braid groups. https://arxiv.org/abs/2105.07848

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