An infinite family of tight triangulations of manifolds

We give explicit construction of vertex-transitive tight triangulations of d-manifolds for d ≥ 2. More explicitly, for each d ≥ 2, we construct two (d + 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. MSC 2000 : 57Q15, 57R05.