Seminar

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The census of orientable cusped hyperbolic 3-manifolds, like the census of knots, enumerates all orientable cusped finite-volume hyperbolic 3-manifolds. Just as the census of knots is arranged by the minimal number of crossings in planar diagrams of knots, the census of orientable cusped hyperbolic 3-manifolds is typically arranged by the minimal number of tetrahedra in triangulations of 3-manifolds. The most widely used “SnapPea census” of orientable cusped hyperbolic 3-manifolds was created in 1989 and continuously expanded afterwards, while its completeness was left undetermined until 2014, when Burton expanded the census to 9 tetrahedra and proved that it is complete without repetition using algebraic tools. In this talk, I will talk about the expansion of the census to 10 and 11 tetrahedra using a more recently developed tool, the verified canonical triangulation, and various applications of the new censuses, including the precisely 439,898 and 1,340,930 exceptional Dehn fillings on them, the next 1849 and 4673 simplest hyperbolic knot exteriors in the 3-sphere, and the first three simplest examples of orientable cusped hyperbolic 3-manifolds containing a closed totally geodesic surface.