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 (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 Kühnelʼs complexes, our manifolds are orientable in even dimensions and non-orientable in odd dimensions.