Hyperbolic homology 3-spheres from drum polyhedra (Q6632139)

In this paper, the authors construct two families of hyperbolic homology spheres. One construction is by Dehn surgery on links with many components but linked with few other components and the other is by surgery on knots. It seems there are some relations between these two families since they have arbitrarily close volume (Corollary 7.7).\N\NThe idea of construction is as follows. The authors start by considering big hyperbolic polyhedra obtained by stacking a large number of ideal drum polyhedra with basis a polygon with many edges. Then they construct the hyperbolic links which are examples of fully augmented links using Bridgeman surgery and Adams' moves in hyperbolic geometry. This construction allows the authors to get some geometric properties, such as geometric convergence to \(\mathbb{H}^{3}\) and arbitrarily large Heegaard genus.