Related papers: Geodesic knots in cusped hyperbolic 3-manifolds

Recent works [MMO1, arXiv:1802.03853, arXiv:1802.04423, arXiv:2101.08956] have shed light on the topological behavior of geodesic planes in the convex core of a geometrically finite hyperbolic 3-manifolds $M$ of infinite volume. In this…

We prove that every closed oriented 3-manifold admits a hyperbolic cone-manifold structure with cone-angle arbitrarily close to 2pi.

We construct examples of hyperbolic rational homology spheres and hyperbolic knot complements in rational homology spheres containing closed embedded totally geodesic surfaces.

We prove that for hyperbolic fibered knots in any closed, connected, oriented 3-manifold the volume and genus are unrelated. As an application we answer a question of Hirose, Kalfagianni, and Kin about volumes of mapping tori that are…

Let $M_0$ be a compact and orientable 3-manifold. After capping off spherical boundaries with balls and removing any torus boundaries, we prove that the resulting manifold $M$ contains handlebodies of arbitrary genus such that the closure…

Extending methods first used by Casson, we show how to verify a hyperbolic structure on a finite triangulation of a closed 3-manifold using interval arithmetic methods. A key ingredient is a new theoretical result (akin to a theorem by…

The main result is that if an Anosov flow in a closed hyperbolic three manifold is not R-covered, then the flow is a quasigeodesic flow. We also prove that if a hyperbolic three manifold supports an Anosov flow, then up to a double cover it…

We enumerate a necessary condition for the existence of infinitely many geometrically distinct, non-constant, prime closed geodesics on an arbitrary closed Riemannian manifold $M$. That is, we show that any Riemannian metric on $M$ admits…

Twisted torus knots and links are given by twisting adjacent strands of a torus link. They are geometrically simple and contain many examples of the smallest volume hyperbolic knots. Many are also Lorenz links. We study the geometry of…

In this paper, we prove that profinitely rigid finite-volume hyperbolic manifolds form a closed set under geometric topology. This observation implies the profinite rigidity of a large family of cusped hyperbolic manifolds via…

We show that a Kleinian surface group, or hyperbolic 3-manifold with a cusp-preserving homotopy-equivalence to a surface, has bounded geometry if and only if there is an upper bound on an associated collection of coefficients that depend…

We introduce the notion of a topological geodesic in a 3-manifold. Under suitable hypotheses on the fundamental group, for instance word-hyperbolicity, topological geodesics are shown to have the useful properties of, and play the same role…

We construct a countable collection of one-parameter families of non-rotational minimal annuli with free boundary in geodesic balls of hyperbolic 3-space. Every surface within a given family shares a common prismatic symmetry group, and…

In a recent paper, Chen, Erchenko and Gogolev have proven that if a Riemannian manifold with boundary has hyperbolic geodesic trapped set, then it can be embedded into a compact manifold whose geodesic flow is Anosov. They have to introduce…

To a hyperbolic manifold one can associate a canonical projective structure and ask whether it can be deformed or not. In a cusped manifold, one can ask about the existence of deformations that are trivial on the boundary. We prove that if…

We show that, on a complete and possibly non-compact Riemannian manifold of dimension at least 2 without close conjugate points at infinity, the existence of a closed geodesic with local homology in maximal degree and maximal index growth…

In this paper, we will use Kahn-Markovic's almost totally geodesic surfaces to construct certain $\pi_1$-injective 2-complexes in closed hyperbolic 3-manifolds. Such 2-complexes are locally almost totally geodesic except along a…

We prove that a closed negatively curved analytic Riemannian manifold that contains infinitely many totally geodesic hypersurfaces is isometric to an arithmetic hyperbolic manifold. Equivalently, any closed analytic Riemannian manifold with…

Let $(M, \partial M)$ be a compact 3-manifold with boundary, which admits a convex co-compact hyperbolic metric. We consider the hyperbolic metrics on $M$ such that the boundary is smooth and strictly convex. We show that the induced…

In this paper we examine the geometry of minimal surfaces of arithmetic hyperbolic 3-manifolds. In particular, we give bounds on the totally geodesic 2-systole, construct infinitely many incommensurable manifolds with the same initial…