Related papers: Cusp transitivity in hyperbolic 3-manifolds
The minimal volume of orientable hyperbolic manifolds with a given number of cusps has been found for $0,1,2,4$ cusps, while the minimal volume of 3-cusped orientable hyperbolic manifolds remains unknown. By using guts in sutured manifolds…
We show that for any integers k and g, with g at least two, there are infinitely many closed hyperbolic 3-manifolds which are integral homology spheres with Casson invariant k, and Heegaard genus equal to g. This existence result is shown…
In the early 2000s, Frigerio, Martelli, and Petronio studied $3$-manifolds of smallest combinatorial complexity that admit hyperbolic structures. As part of this work they defined and studied the class $M_{g,k}$ of smallest complexity…
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 orientable finite-volume hyperbolic 3-manifolds having non-empty compact totally geodesic boundary and admitting an ideal triangulation with at most four tetrahedra. We also compute the volume of all such manifolds, we…
This paper describes a general algorithm for finding the commensurator of a non-arithmetic cusped hyperbolic manifold, and for deciding when two such manifolds are commensurable. The method is based on some elementary observations regarding…
For X = R, C, or H it is well known that cusp cross-sections of finite volume X-hyperbolic (n+1)-orbifolds are flat n-orbifolds or almost flat orbifolds modelled on the (2n+1)-dimensional Heisenberg group N_{2n+1} or the (4n+3)-dimensional…
McReynolds showed that every compact Nil 3-manifold occurs as the cusp cross-section of some arithmetic complex hyperbolic 2-manifold. We classify which commensurability classes of cusped, arithmetic, complex hyperbolic 2-manifolds admit…
A group $G$ is called subgroup conjugacy separable if for every pair of non-conjugate finitely generated subgroups of $G$, there exists a finite quotient of $G$ where the images of these subgroups are not conjugate. It is proved that the…
We construct here two new examples of non-orientable, non-compact, hyperbolic 4-manifolds. The first has minimal volume $v_m = 4{\pi}^2/3$ and two cusps. This example has the lowest number of cusps among known minimal volume hyperbolic…
Three dimensional hyperbolic manifolds have accumulation points in the spectrum of their volumes, leading to a divergence in the sum over topologies. The limit points are cusped hyperbolic manifolds, and we propose to renormalize the sum by…
An action of a group $G$ is highly transitive if $G$ acts transitively on $k$-tuples of distinct points for all $k \geq 1$. Many examples of groups with a rich geometric or dynamical action admit highly transitive actions. We prove that if…
Given a cusped hyperbolic 3-manifold with finite volume, we define two types of complex parameters which capture geometric information about the preimages of geodesic arcs traveling between cusp cross-sections. We prove that these…
We find that cusp densities of hyperbolic knots in the 3-sphere are dense in [0,0.6826...] and those of links are dense in [0,0.853...]. We define a new invariant associated with cusp volume, the cusp crossing density, as the ratio between…
This paper presents some finiteness results for the number of boundary slopes of immersed essential surfaces of given genus g in a compact 3-manifold with torus boundary. In the case of hyperbolic 3-manifolds we obtain uniform quadratic…
We prove that every cusped hyperbolic 3-manifold has a finite cover admitting infinitely many geometric ideal triangulations. Furthermore, every long Dehn filling of one cusp in this cover admits infinitely many geometric ideal…
We study projective deformations of (topologically finite) hyperbolic 3-orbifolds whose ends have turnover cross section. These deformations are examples of projective cusp openings, meaning that hyperbolic cusps are deformed in the…
The waist size of a cusp in an orientable hyperbolic 3-manifold is the length of the shortest nontrivial curve generated by a parabolic isometry in the maximal cusp boundary. Previously, it was shown that the smallest possible waist size,…
In all dimensions $n \ge 5$, we prove the existence of closed orientable hyperbolic manifolds that do not admit any $\text{spin}^c$ structure, and in fact we show that there are infinitely many commensurability classes of such manifolds.…
A version of a conjecture of McMullen is as follows: Given a hyperbolizable 3-manifold M with incompressible boundary, there exists a uniform constant K such that if N is a hyperbolic 3-manifold homeomorphic to the interior of M, then the…