|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||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).
|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
Show full item record
checked on Feb 4, 2023
checked on Feb 5, 2023
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.