  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. We also provide some evidence for the
conjecture that each n-dimensional, compact smooth manifold M^n (n>1), admits a
totally skew embedding in the Euclidean space of dimension N = 4n-2alpha(n)+1
where alpha(n)=number of non-zero digits in the binary representation of n.
This is a revised version of the paper (accepted for publication in A.M.S.
Transactions).
