On minimal ideal triangulations of cusped hyperbolic 3-manifolds

William Jaco, Hyam Rubinstein, Jonathan Spreer and Stephan Tillmann

Abstract

Previous work of the authors studies minimal triangulations of closed 3-manifolds using a characterisation of low degree edges, embedded layered solid torus subcomplexes and 1-dimensional ${\mathbb{Z}}_2$-cohomology. The underlying blueprint is now used in the study of minimal ideal triangulations. As an application, it is shown that the monodromy ideal triangulations of the hyperbolic once-punctured torus bundles are minimal.

AMS Subject Classification: Primary 57Q15; secondary 57N10, 57M50, 57M27.