On the embeddability of skeleta of manifold triangulations

We show a criterion for a skeleton of a manifold triangulation being embeddable into Euclidean space in terms of the complement of a submanifold. As an application, we obtain embeddability of a $(q-1)$-skeleton of a triangulation of an $S^p$-bundle over $S^q$ into ${\mathbb{R}}^{p+q}$.