On geometrically realizable Möbius triangulations (Q432714)
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scientific article; zbMATH DE number 6053074
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On geometrically realizable Möbius triangulations |
scientific article; zbMATH DE number 6053074 |
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On geometrically realizable Möbius triangulations (English)
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4 July 2012
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linking number
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map
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cycle
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Möbius band
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The title refers to triangulations of the Möbius band. A Möbius triangulation that is geometrically non-realizable in 3-space (with straight edges) was found by \textit{U. Brehm} [Proc. Am. Math. Soc. 89, 519--522 (1983; Zbl 0526.57013). This is based on the linking of certain cycles of length 3.NEWLINENEWLINE In the paper under review the authors characterize this phenomenon more systematically. Theorem 2 states that a Möbius triangulation is geometrically realizable if and only if there are no two disjoint cycles of length 3 that are homotopic to the boundary of the Möbius band.
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