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 2 + 5 d + 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 2 d + 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.