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The van Kampen-Flores theorem states that the $d$-skeleton of a$(2d+2)$-simplex does not embed into $\mathbb{R}^{2d}$. We prove the vanKampen-Flores theorem for triangulations of manifolds satisfying a certaincondition on their Stiefel-Whitney classes. In particular, we show that the$d$-skeleton of a triangulation of a $(2d+1)$-manifold with non-trivial totalStiefel-Whitney class does not embed into $\mathbb{R}^{2d}$.

Van Kampen-Flores theorem and Stiefel-Whitney classes