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Abstract: Following Ghomi and Tabachnikov we study topological obstructions to totallyskew embeddings of a smooth manifold M in Euclidean spaces. This problem isnaturally related to the question of estimating the geometric dimension of thestable normal bundle of the configuration space F 2M of ordered pairs ofdistinct points in M. We demonstrate that in a number of interesting cases thelower bounds obtained by this method are quite accurate and very close to thebest known general upper bound. We also provide some evidence for theconjecture that each n-dimensional, compact smooth manifold M^n n>1, admits atotally skew embedding in the Euclidean space of dimension N = 4n-2alphan+1where alphan=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.



Author: Djordje Baralic, Branislav Prvulovic, Gordana Stojanovic, Sinisa Vrecica, Rade Zivaljevic

Source: https://arxiv.org/







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