A tightness criterion for homology manifolds with or without boundary

Generalizing the previously known combinatorial criteria for tightness, we prove that, for any field F, all k-stacked and (k+1)-neighbourly F-homology manifolds M are F-tight. The only condition is that, in case char(F)≠2 and M is without boundary, M must be orientable. This provides a complete answer to a recent question of Effenberger.