Geometric Realization of a Triangulation on the Projective Plane with One Face Removed |
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| Authors: | C. Paul Bonnington Atsuhiro Nakamoto |
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| Affiliation: | (1) Department of Mathematics, University of Auckland, Auckland, New Zealand;(2) Department of Mathematics, Yokohama National University, Yokohama 240-8501, Japan |
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| Abstract: | Let M be a map on a surface F 2. A geometric realization of M is an embedding of F 2 into a Euclidean 3-space ?3 such that each face of M is a flat polygon. We shall prove that every triangulation G on the projective plane has a face f such that the triangulation of the Möbius band obtained from G by removing the interior of f has a geometric realization. |
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| Keywords: | Triangulation Geometric realization M?bius band Projective plane |
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