Polytopal Bier Spheres and Kantorovich–Rubinstein Polytopes of Weighted Cycles
| Autor: | Filip D. Jevtić, Marinko Timotijević, Rade T. Živaljević |
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| Rok vydání: | 2019 |
| Předmět: |
Triangulation (topology)
050101 languages & linguistics 05 social sciences Boundary (topology) Polytope 02 engineering and technology Theoretical Computer Science Connection (mathematics) Combinatorics Simplicial complex Computational Theory and Mathematics Convex polytope 0202 electrical engineering electronic engineering information engineering Mathematics::Metric Geometry Discrete Mathematics and Combinatorics 020201 artificial intelligence & image processing 0501 psychology and cognitive sciences SPHERES Geometry and Topology Mathematics |
| Zdroj: | Discrete & Computational Geometry. 65:1275-1286 |
| ISSN: | 1432-0444 0179-5376 |
| DOI: | 10.1007/s00454-019-00151-5 |
| Popis: | The problem of deciding if a given triangulation of a sphere can be realized as the boundary sphere of a simplicial, convex polytope is known as the ‘Simplicial Steinitz problem’. It is known by an indirect and non-constructive argument that a vast majority of Bier spheres are non-polytopal. Contrary to that, we demonstrate that the Bier spheres associated to threshold simplicial complexes are all polytopal. Moreover, we show that all Bier spheres are starshaped. We also establish a connection between Bier spheres and Kantorovich–Rubinstein polytopes by showing that the boundary sphere of the KR-polytope associated to a polygonal linkage (weighted cycle) is isomorphic to the Bier sphere of the associated simplicial complex of “short sets”. |
| Databáze: | OpenAIRE |
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