ON THE HOMOLOGY OF THE COMMUTATOR SUBGROUP OF THE PURE BRAID GROUP

摘要

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 <= l <= n - 2. As a consequence we determine the cohomological dimension of [P-n, P-n]: for n >= 2 we have cd([P-n, P-n]) = n - 2.