Geodesic
ℤ2–Thurston norm and complexity of 3–manifolds, II
Jaco, William1 ; Rubinstein, Hyam2 ; Spreer, Jonathan3 ; Tillmann, Stephan3
1Department of Mathematics, Oklahoma State University, Stillwater, OK, United States
2Department of Mathematics and Statistics, The University of Melbourne, Parkville, VIC, Australia
3School of Mathematics and Statistics, The University of Sydney, Sydney, NSW, Australia
Algebraic and Geometric Topology, Tome 20 (2020) no. 1, pp. 503-529
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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(ℝ).

DOI : 10.2140/agt.2020.20.503
Classification : 57N10, 57Q15, 57M27, 57M50
Keywords: 3–manifold, minimal triangulation, layered triangulation, efficient triangulation, complexity, Seifert fibred space, lens space

Jaco, William  1   ; Rubinstein, Hyam  2   ; Spreer, Jonathan  3   ; Tillmann, Stephan  3

1 Department of Mathematics, Oklahoma State University, Stillwater, OK, United States
2 Department of Mathematics and Statistics, The University of Melbourne, Parkville, VIC, Australia
3 School of Mathematics and Statistics, The University of Sydney, Sydney, NSW, Australia 
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Jaco, William; Rubinstein, Hyam; Spreer, Jonathan; Tillmann, Stephan. ℤ2–Thurston norm and complexity of 3–manifolds, II. Algebraic and Geometric Topology, Tome 20 (2020) no. 1, pp. 503-529. doi: 10.2140/agt.2020.20.503

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