Gromov's Conjecture for Product of Baumslag-Solitar groups and some other One-relator groups

Abstract

We show that Baumslag-Solitar groups are virtually 2-avoidable, that is, they admit finite index subgroup whose first homology is devoid of $\mathbb{Z}_2$ summand. We also prove virtual 2-avoidability for some other classes of one-relator groups, which generalizes non-orientable surface groups. This along with result from a previous paper confirms Gromov's Conjecture about macroscopic dimension of universal cover of PSC manifolds, for all closed oriented spin manifolds whose fundamental group is product of Baumslag-Solitar groups, the one-relator groups under consideration.