Minimal 4-colored graphs representing an infinite family of hyperbolic 3-manifolds
| Autor: | Evgeny Fominykh, Paola Cristofori, Michele Mulazzani, Vladimir Tarkaev |
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| Přispěvatelé: | Cristofori, Paola, Fominykh, Evgeny, Mulazzani, Michele, Tarkaev, Vladimir |
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
graph complexity
Computation Colored graph 010103 numerical & computational mathematics 01 natural sciences 3-Manifolds Colored graphs Graph complexity Tetrahedral manifolds Combinatorics Mathematics - Geometric Topology FOS: Mathematics 3-manifolds colored graphs graph complexity tetrahedral manifolds 0101 mathematics Invariant (mathematics) tetrahedral manifolds Mathematics::Symplectic Geometry Mathematics 57N10 57Q15 57M15 Algebra and Number Theory Applied Mathematics 010102 general mathematics colored graphs Geometric Topology (math.GT) Graph 3-manifolds Computational Mathematics Tetrahedron Geometry and Topology Mathematics::Differential Geometry Analysis |
| Popis: | The graph complexity of a compact 3-manifold is defined as the minimum order among all 4-colored graphs representing it. Exact calculations of graph complexity have been already performed, through tabulations, for closed orientable manifolds (up to graph complexity 32) and for compact orientable 3-manifolds with toric boundary (up to graph complexity 12) and for infinite families of lens spaces. In this paper we extend to graph complexity 14 the computations for orientable manifolds with toric boundary and we give two-sided bounds for the graph complexity of tetrahedral manifolds. As a consequence, we compute the exact value of this invariant for an infinite family of such manifolds. Comment: 13 pages, 4 figures, 1 table. Minor changes suggested by referee. Published online 01 December 2017 in RACSAM |
| Databáze: | OpenAIRE |
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