2012/10/03 by Basudeb Datta, Datta, Basudeb, Nitin Singh +1 · 1 citation
Computer Science · Mathematics · #Topological and Geometric Data Analysis #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models
paper · doi:10.48550/arxiv.1210.1045
We give an explicit construction of vertex-transitive tight triangulations of d-manifolds for d≥ 2. More explicitly, for each d≥ 2, we construct two (d2+5d+5)-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 2d+3 vertices constructed by Kühnel. The manifolds we construct are strongly minimal. For d≥ 3, they are also tight neighborly as defined by Lutz, Sulanke and Swartz. Like Kühnel's complexes, our manifolds are orientable in even dimensions and non-orientable in odd dimensions.