Mod 2 cohomology of the Grassmann manifold G 2,n is a polynomial algebra modulo a certain well-known ideal. A Groebner basis for this ideal is obtained. Using this basis, some new immersion results for Grassmannians G 2,n are established.
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 ) ≤ 4n+1 established by Ghomi and Tabachnikov. We also provide some evidence for the conjecture that for every n-dimensional, compact smooth manifold M n (n > 1),
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