Asian Journal of Mathematics
Volume 21 (2017)
A new combinatorial class of $3$-manifold triangulations
Pages: 543 – 570
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.
$3$-manifold, triangulation, $0$-efficient, circle-valued angle structure
2010 Mathematics Subject Classification
Paper received on 8 July 2014.