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Tight polyhedral Klein bottles, projective planes, and Möbius bands. (English) Zbl 0275.57005


MSC:

57Q35 Embeddings and immersions in PL-topology
57N05 Topology of the Euclidean \(2\)-space, \(2\)-manifolds (MSC2010)
57M20 Two-dimensional complexes (manifolds) (MSC2010)
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References:

[1] Banchoff, T.: Tightly embedded two-dimensional polyhedral manifolds. Amer. J. of Math.87, 462-472 (1965) · Zbl 0136.21005 · doi:10.2307/2373013
[2] Banchoff, T.: The two-piece property and tightn-manifolds with boundary inE n . Trans. A.M.S.161, 259-267 (1971) · Zbl 0229.53055
[3] Franklin, P.: A six color problem. J. Math. Phys.13, 363-369 (1934) · Zbl 0010.27502
[4] Kuiper, N.: On surfaces in euclidean three-space. Bull. Math. Soc. Belg.12, 5-22 (1960) · Zbl 0196.25901
[5] Kuiper, N.: On convex maps. Nieuw Archief-Voor Wisk.10, 147-164 (1962) · Zbl 0112.36502
[6] Kuiper, N.: Tight topological embeddings of the Möbius band. J. Diff. Geom.6, 271-283 (1972) · Zbl 0234.53048
[7] Ringel, G.: Bestimmung der Maximumzahl der Nachbargebiete auf nichtorientierbaren Flächen. Math. Ann.127, 181-214 (1954) · Zbl 0055.17001 · doi:10.1007/BF01361120
[8] Ringel, G., Youngs, J.W.T.: Solution of the Heawood map-coloring problem. Proc. Nat. Acad. Sci.60, 438-445 (1968) · Zbl 0155.51201 · doi:10.1073/pnas.60.2.438
[9] Rodriguez, L.: Thesis, Brown University 1972
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