Veering triangulations admit strict angle structures. (English) Zbl 1246.57034

The authors introduce a weaker notion of the concept of a veering taut triangulation of a \(3\)-manifold, recently introduced by I. Agol in his preprint [Ideal triangulations of pseudo-Anosov mapping tori, arXiv:1008.1606]. They use this weaker version in order to show that all veering triangulations admit strict angle structures. In particular, this then allows to show that there exist veering taut triangulations which are not layered (in fact the manifolds in this type of examples are not fibred over the circle). This answers a question asked by I. Agol.


57M50 General geometric structures on low-dimensional manifolds


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[1] I Agol, Ideal triangulations of pseudo-Anosov mapping tori · Zbl 1335.57026
[2] K S Brown, Trees, valuations, and the Bieri-Neumann-Strebel invariant, Invent. Math. 90 (1987) 479 · Zbl 0663.20033 · doi:10.1007/BF01389176
[3] B Burton, Regina: Normal surface and \(3\)-manifold topology software (1999-2009)
[4] J O Button, Fibred and virtually fibred hyperbolic \(3\)-manifolds in the censuses, Experiment. Math. 14 (2005) 231 · Zbl 1085.57012 · doi:10.1080/10586458.2005.10128920
[5] N Dunfield, Which cusped census manifolds fiber? (2010)
[6] F Guéritaud, On canonical triangulations of once-punctured torus bundles and two-bridge link complements, Geom. Topol. 10 (2006) 1239 · Zbl 1130.57024 · doi:10.2140/gt.2006.10.1239
[7] W Jaco, U Oertel, An algorithm to decide if a \(3\)-manifold is a Haken manifold, Topology 23 (1984) 195 · Zbl 0545.57003 · doi:10.1016/0040-9383(84)90039-9
[8] W Jaco, J H Rubinstein, \(0\)-efficient triangulations of \(3\)-manifolds, J. Differential Geom. 65 (2003) 61 · Zbl 1068.57023
[9] E Kang, J H Rubinstein, Ideal triangulations of 3-manifolds II; taut and angle structures, Algebr. Geom. Topol. 5 (2005) 1505 · Zbl 1096.57018 · doi:10.2140/agt.2005.5.1505
[10] M Lackenby, Taut ideal triangulations of \(3\)-manifolds, Geom. Topol. 4 (2000) 369 · Zbl 0958.57019 · doi:10.2140/gt.2000.4.369
[11] F Luo, S Tillmann, Angle structures and normal surfaces, Trans. Amer. Math. Soc. 360 (2008) 2849 · Zbl 1152.57004 · doi:10.1090/S0002-9947-08-04301-8
[12] J L Tollefson, Normal surface \(Q\)-theory, Pacific J. Math. 183 (1998) 359 · Zbl 0930.57017 · doi:10.2140/pjm.1998.183.359
[13] J R Weeks, SnapPea: A computer program for creating and studying hyperbolic \(3\)-manifolds
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