2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/226325We compute lower bounds on the virtual crossing number and minimal surface genus of virtual knot diagrams from the arrow polynomial. In particular, we focus on several interesting examples.17 Pages, 18 figures and 7 tablesGeometric Topology57M27Lower bounds on virtual crossing number and minimal surface genustext