Following Ghomi and Tabachnikov we study topological obstructions to totally
skew embeddings of a smooth manifold M in Euclidean spaces. This problem is
naturally related to the question of estimating the geometric dimension of the
stable normal bundle of the configuration space F_2(M) of ordered pairs of
distinct points in M. We demonstrate that in a number of interesting cases the
lower bounds obtained by this method are quite accurate and very close to the
best known general upper bound.