${\mathbb{Z}}_2$-Thurston Norm and Complexity of 3-Manifolds, II

William Jaco, Hyam Rubinstein, Jonathan Spreer and Stephan Tillmann

Abstract

In this sequel to earlier papers by three of the authors, we obtain a new bound on the complexity of a closed 3–manifold, as well as a characterisation of manifolds realising our complexity bounds. As an application, we obtain the first infinite families of minimal triangulations of Seifert fibred spaces modelled on Thurston's geometry $\widetilde{{\mathrm{SL}}_2(\mathbb{R})}$.

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