Quasitoric manifolds and Small covers over properly colored polytopes: Immersions and Embeddings

2014/06/18 by Djordje Baralić, Baralic, Djordje, Vladimir Grujić +1
Computer Science · Mathematics · #52B05 #52B12 #57N35 #57N65 #Advanced Combinatorial Mathematics #Algebraic Topology (math.AT) #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #FOS: Mathematics #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1406.4722

openalex publication_date 2014/06/18 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We construct small covers and quasitoric manifolds over n-dimensional simple polytopes which allow proper colorings of facets with n colors. We calculate Stiefel-Whitney classes of these manifolds as obstructions to immersions and embeddings into Euclidean spaces. The largest dimension required for embedding is achieved in the case n is a power of two.

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