2013/04/22 by Djordje Baralić, Djordje Baralic, Baralic, Djordje
Mathematics · #13F20 #52B11 #57N35 #57R40 #Advanced Combinatorial Mathematics #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AC #math.AT #msc:13F20 #msc:52B11 #msc:57N35 #msc:57R40
paper · pdf · doi:10.48550/arxiv.1304.5924
11 pages, 5 fiures
arxiv created 2013/04/22 · openalex publication_date 2013/04/22 · arxiv updated 2013/04/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Totally skew embeddings are introduced by Ghomi and Tabachnikov. They are naturally related to classical problems in topology, such as the generalized vector field problem and the immersion problem for real projective spaces. In recent paper Topological obstructions to totally skew embeddings, totaly skew embeddings are studied by using the Stiefel-Whitney classes In the same paper it is conjectured that for every n-dimensional, compact smooth manifold Mn (n>1), N(Mn)≤ 4n-2α(n)+1, where N(Mn) is defined as the smallest dimension N such that there exists a \em totally skew embedding of a smooth manifold Mn in ℝN. We prove that for every n, there is a quasitoric manifold Q2n for which the orbit space of Tn action is a cube In and N(Q2n)≥ 8n-4α(n)+1. Using the combinatorial properties of cohomology ring H^* (Q2n, ℤ2), we construct an interesting general non-trivial example different from known example of the product of complex projective spaces.