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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 SL˜2().

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
References
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