We prove that there are at least two commensurability classes of (cusped, arithmetic) minimal-volume hyperbolic –manifolds. Moreover, by applying a well-known technique due to Gromov and Piatetski-Shapiro, we build the smallest known nonarithmetic hyperbolic –manifold.
"New hyperbolic $4$–manifolds of low volume." Algebr. Geom. Topol. 19 (5) 2653 - 2676, 2019. https://doi.org/10.2140/agt.2019.19.2653