A new combinatorial class of 3-manifold triangulations
arXiv:1312.5087
Abstract
We define a new combinatorial class of triangulations of closed 3-manifolds, satisfying a weak version of 0-efficiency combined with a weak version of minimality, and study them using twisted squares. As an application, we obtain strong restrictions on the topology of a 3-manifold from the existence of non-smooth maxima of the volume function on the space of circle-valued angle structures.
28 pages, 23 figures; colour printing recommended; to appear in AJM