GEOMETRIC REALIZATION OF MOEBIUS TRIANGULATIONS

摘要

A Moebius triangulation is a triangulation on the Mobius band. A geometric realization of a map M on a surface Σ is an embedding of Σ into a Euclidean 3-space 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 Moebius 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 Mobius triangulation G - f obtained from G by removing the interior of f has a geometric realization.