Abstract
Following Ghomi and Tabachnikov's 2008 work, we study the invariant N(M-n) defined as the smallest dimension N such that there exists a totally skew embedding of a smooth manifold M-n in R-N. 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-n) of ordered pairs of distinct points in M-n. We demonstrate that in a number of interesting cases the lower bounds on N(M-n) obtained by this method are quite accurate and very close to the best known general upper bound N(M-n) 1), N(M-n) <= 4n - 2 alpha(n) + 1.
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