#### Volume 20, issue 1 (2020)

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$\mathbb{Z}_2$–Thurston norm and complexity of $3$–manifolds, II

### William Jaco, J Hyam Rubinstein, Jonathan Spreer and Stephan Tillmann

Algebraic & Geometric Topology 20 (2020) 503–529
##### 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 ${\stackrel{˜}{SL}}_{2}\left(ℝ\right)$.

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##### Keywords
3–manifold, minimal triangulation, layered triangulation, efficient triangulation, complexity, Seifert fibred space, lens space
##### Mathematical Subject Classification 2010
Primary: 57N10, 57Q15
Secondary: 57M27, 57M50