On the homology of the commutator subgroup of the pure braid group
Abstract
We study the homology of $[P_n,P_n]$, the commutator subgroup of the pure braid group on $n$ strands, and show that $H_l([P_n,P_n])$ contains a free abelian group of infinite rank for all $1\leq l\leq n-2$. As a consequence we determine the cohomological dimension of $[P_n,P_n]$: for $n\geq 2$ we have $\mathrm{cd}([P_n,P_n])=n-2$.
- Publication:
-
arXiv e-prints
- Pub Date:
- May 2019
- DOI:
- 10.48550/arXiv.1905.05099
- arXiv:
- arXiv:1905.05099
- Bibcode:
- 2019arXiv190505099B
- Keywords:
-
- Mathematics - Algebraic Topology;
- Mathematics - K-Theory and Homology;
- 20F36;
- 55R20;
- 55R35;
- 55R80;
- 16S34;
- 20C07
- E-Print:
- 21 pages