An infinite family of tight triangulations of manifolds

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• 作者：Basudeb Datta ; Nitin Singh
• 关键词：Stacked sphere ; Tight triangulation ; Strongly minimal triangulation
• 刊名：Journal of Combinatorial Theory, Series A
• 出版年：2013
• 出版时间：November, 2013
• 年：2013
• 卷：120
• 期：8
• 页码：2148-2163
• 全文大小：437 K

文摘

We give explicit construction of vertex-transitive tight triangulations of d-manifolds for . More explicitly, for each , we construct two -vertex neighborly triangulated d-manifolds whose vertex-links are stacked spheres. The only other non-trivial series of such tight triangulated manifolds currently known is the series of non-simply connected triangulated d-manifolds with vertices constructed by K¨¹hnel. The manifolds we construct are strongly minimal. For , they are also tight neighborly as defined by Lutz, Sulanke and Swartz. Like K¨¹hnel?s complexes, our manifolds are orientable in even dimensions and non-orientable in odd dimensions.