Basudeb Datta, Indian Institute of Science

PDL C-401

Stacked triangulated manifolds are generalizations of stacked spheres. For dimension \$d\geq 4\$, stacked \$d\$-manifolds are same as locally stacked manifolds. Not all locally stacked 3-manifolds are stacked. Recently, we have shown that every stacked triangulation of a closed manifold (for any dimension) is obtained from the boundary of a simplex by certain combinatorial operations.

Tight triangulated manifolds are generalisations of neighborly triangulations of closed surfaces. Tight triangulated manifolds are conjectured to be minimal. It is known that locally stacked tight triangulated manifolds are strongly minimal. From recent works, we know some infinite series of tight triangulated manifolds. All these examples are stacked. Very few tight triangulated manifolds are known which are not stacked. Recently, we have shown that a triangulation of a closed 3-manifold is tight if and only if it is neighbourly and stacked.

In this talk, I would like to discuss these are some related results.