Satyanath Howladar | Searcharxiv

arXiv2025

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

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.

math.GR↗

arXiv2023

On Gromov's conjecture for right-angled Artin groups

We prove that the universal covering $\Wi M$ of an $n$-dimensional closed spin PSC manifold $M$ whose fundamental group $\pi_1(M)$ is a right-angled Artin group has macroscopic dimension $\dim_{mc}\Wi M\le n-2$. This confirms Gromov's conjecture in the case of right-angled Artin groups.

math.GT↗