#### 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 ${\stackrel{˜}{SL}}_{2}\left(ℝ\right)$.

##### 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
##### Publication
Received: 29 April 2019
Revised: 11 July 2019
Accepted: 30 July 2019
Published: 23 February 2020
##### Authors
 William Jaco Department of Mathematics Oklahoma State University Stillwater, OK United States J Hyam Rubinstein Department of Mathematics and Statistics The University of Melbourne Parkville, VIC Australia Jonathan Spreer School of Mathematics and Statistics The University of Sydney Sydney, NSW Australia Stephan Tillmann School of Mathematics and Statistics The University of Sydney Sydney, NSW Australia