2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/164178We define "fat" train tracks and use them to give a combinatorial criterion for the Hempel distance of Heegaard splittings for closed orientable 3-manifolds. We apply this criterion to 3-manifolds obtained from surgery on knots in the three sphere.25 pages no figures. to appear in Proceedings of "Knots Groups and 3-manifolds" Marseilles France 2006Geometric Topologytext