Tight and stacked triangulations of manifolds

Wednesday 29 July 2015 from 11:00–12:00 in Carslaw 535A

Please join us for lunch after the talk!

Abstract: Tight triangulated manifolds are generalisations of neighborly triangulations of closed surfaces and are interesting objects in Combinatorial Topology. Tight triangulated manifolds are conjectured to be minimal. It is known that locally stacked tight triangulated manifolds are strongly minimal. With a few exceptions, all the known tight triangulated manifolds are stacked. There are three infinite sequences of stacked triangulated manifolds that are tight.

Recently, we proved that (i) a triangulation of a closed 3-manifold is tight with respect to a field of odd characteristic if and only if it is neighbourly, orientable and stacked, and (ii) a tight-neighborly triangulated 3-manifold is tight. In this talk, we present a survey on recent works on tight triangulation.