Authors: Baralić, Đorđe
Prvulović, Branislav
Stojanović, Gordana
Vrećica, Siniša
Živaljević, Rade 
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Topological obstructions to totally skew embeddings
Journal: Transactions of the American Mathematical Society
Volume: 364
Issue: 4
First page: 2213
Last page: 2226
Issue Date: 31-Jan-2012
Rank: M21
ISSN: 0002-9947
DOI: 10.1090/S0002-9947-2011-05499-1
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).
Publisher: American Mathematical Society
Project: Geometry and Topology of Manifolds, Classical Mechanics and Integrable Dynamical Systems 
Topology, geometry and global analysis on manifolds and discrete structures 

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