Related papers: Creating subdivision rules from polyhedra with ide…

In a recent paper Garoufalidis and Reid constructed pairs of 1-cusped hyperbolic 3-manifolds which are isospectral but not isometric. In this paper we extend this work to the multi-cusped setting by constructing isospectral but not…

For a single cusped hyperbolic 3-manifold, Hodgson proved that there are only finitely many Dehn fillings of it whose trace fields have bounded degree. In this paper, we conjecture the same for manifolds with more cusps, and give the first…

In this article, we prove that the commensurability class of a closed, orientable, hyperbolic 3-manifold is determined by the surface subgroups of its fundamental group. Moreover, we prove that there can be only finitely many closed,…

We construct a hyperbolic three-manifold with trivial finite type invariants up to a given degree.

We classify the 3-dimensional hyperbolic polyhedral orbifolds that contain no embedded essential 2-suborbifolds, up to decomposition along embedded hyperbolic triangle orbifolds (turnovers). We give a necessary condition for a 3-dimensional…

It is conjectured that every cusped hyperbolic 3-manifold admits a geometric triangulation, i.e. it is decomposed into positive volume ideal hyperbolic tetrahedra. Here, we show that sufficiently highly twisted knots admit a geometric…

We enumerate all spaces obtained by gluing in pairs the faces of the octahedron in an orientation-reversing fashion. Whenever such a gluing gives rise to non-manifold points, we remove small open neighbourhoods of these points, so we…

In this paper we will consider the 2-fold symmetric complex hyperbolic triangle groups generated by three complex reflections through angle 2pi/p with p no smaller than 2. We will mainly concentrate on the groups where some elements are…

The purpose of this paper is to give an application of the gluing theorem for special Lagrangian submanifolds of a Calabi-Yau 3-fold. We proved a gluing theorem before to smooth a codimension-two singularity of a particular special…

We prove a comparison theorem for certain types of polyhedra in a 3-manifold with its scalar curvature bounded below by $-6$. The result confirms in some cases the Gromov dihedral rigidity conjecture in hyperbolic $3$-space.

We extend to the context of hyperbolic 3-manifolds with geodesic boundary Thurston's approach to hyperbolization by means of geometric triangulations. In particular, we introduce moduli for (partially) truncated hyperbolic tetrahedra, and…

Finite subdivision rules in high dimensions can be difficult to visualize and require complex topological structures to be constructed explicitly. In many applications, only the history graph is needed. We characterize the history graph of…

Let $(M, \partial M)$ be a compact 3-manifold with boundary which admits a complete, convex co-compact hyperbolic metric. For each hyperbolic metric $g$ on $M$ such that $\dr M$ is smooth and strictly convex, the induced metric on $\dr M$…

This paper is subsequent to [5]. In this paper, we extend the classification of hyperbolic Dehn fillings with sufficiently large coefficients by addressing the remaining case not covered in [5]. Specifically, by considering the case in…

We prove that there are only finitely many closed hyperbolic 3-manifolds with injectivity radius and first eigenvalue of the Laplacian bounded below whose fundamental groups can be generated by a given number of elements. An application to…

We investigate relation between Dehn fillings and commensurability of hyperbolic 3-manifolds. The set consisting of the commensurability classes of hyperbolic 3-manifolds admits the quotient topology induced by the geometric topology. We…

We show that the aspherical manifolds produced via the relative strict hyperbolization of polyhedra enjoy many group-theoretic and topological properties of open finite volume negatively pinched manifolds, including relative hyperbolicity,…

The main result of this paper is that any $3$-dimensional manifold with a finite group action is equivariantly, invertibly homology cobordant to a hyperbolic manifold; this result holds with suitable twisted coefficients as well. The…

We classify the boundaries of hyperbolic groups that have enough quasiconvex codimension-1 surface subgroups with trivial or cyclic intersections.

We show that the standard method for constructing closed hyperbolic manifolds of arbitrary dimension possessing reflective symmetries typically produces reflections whose fixed point sets are nonseparating.