Co-rank and Betti number of a group
arXiv:1502.02197 · doi:10.1007/s10587-015-0195-0
Abstract
We study the maximal ranks of a free and a free abelian quotients of a finitely generated group, called co-rank (inner rank, cut number) and the Betti number, respectively. We show that any combination of these values within obvious constraints is realized for some finitely presented group, which is important for manifold and foliation topology.
Accepted to: Czechoslovak Mathematical Journal, 2015