Article
Geometric Realization of Möbius Triangulations
Author/s | Chávez de Diego, María José
Fijavz, Gasper Márquez Pérez, Alberto Nakamoto, Atsuhiro Suárez, Esperanza |
Department | Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII) |
Publication Date | 2008 |
Deposit Date | 2016-02-12 |
Published in |
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Abstract | A Möbius triangulation is a triangulation on the Möbius band. A geometric realization of a map M on a surface $\Sigma$ is an embedding of $\Sigma$ into a Euclidean 3-space $\mathbb{R}^3$ such that each face of M is a flat ... A Möbius triangulation is a triangulation on the Möbius band. A geometric realization of a map M on a surface $\Sigma$ is an embedding of $\Sigma$ into a Euclidean 3-space $\mathbb{R}^3$ such that each face of M is a flat polygon. In this paper, we shall prove that every 5-connected triangulation on the Möbius band has a geometric realization. In order to prove it, we prove that if G is a 5-connected triangulation on the projective plane, then for any face f of G, the Möbius triangulation $G-f$ obtained from G by removing the interior of f has a geometric realization. |
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