|Title:||Quasitoric manifolds and small covers over properly coloured polytopes: Immersions and embeddings||Journal:||Sbornik Mathematics||Volume:||207||Issue:||4||First page:||479||Last page:||489||Issue Date:||1-Jan-2016||Rank:||M22||ISSN:||1064-5616||DOI:||10.1070/SM8401||Abstract:||
We construct small covers and quasitoric manifolds over n-dimensional simple polytopes which allow proper colourings of facets with n colours. We calculate the 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.
|Keywords:||Colourings | Embeddings | Quasitoric manifolds | Simple polytopes | Stiefel-Whitney classes||Publisher:||Turpion||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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