Sarah L. Browne,
Maria Paula Gomez Aparicio,
Lauren C. Ruth, and
K-homology and K-theory of pure braid groups
||September 8, 2022.
||pure braid, K-theory, K-homology, Baum-Connes conjecture.
||58B34, 19D55, 46L80, 20F36.
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 on 3-strands.
We thank Alain Valette for the suggestion to examine K-theory and K-homology of pure braid groups. We thank the organizers of the Women in Operator Algebras Conference that took place at BIRS where this project started. HW acknowledges the support from Science and Technology Commission of Shanghai Municipality (STCSM), grant No.18dz2271000. MGA was partially supported by ANR project Singstar.
Universitá degli Studi di Bari
Dipartimento di Matematica
Via E. Orabona 4, 70125 Bari, Italy
Sarah L. Browne:
The University of Kansas
Department of Mathematics
1460 Jayhawk Blvd, Lawrence, KS 66045, USA
Maria Paula Gomez Aparicio:
Université Paris-Saclay, CNRS
Laboratoire de mathématiques d'Orsay
91405, Orsay, France
Lauren C. Ruth:
Dobbs Ferry, NY 10522, USA
School of Mathematical Sciences and Shanghai Key Laboratory of PMMP
East China Normal University
Shanghai 200241, China