Hyperbolic limits of cantor set complements in the sphere

@article{Cremaschi2022HyperbolicLO,
  title={Hyperbolic limits of cantor set complements in the sphere},
  author={Tommaso Cremaschi and Franco Vargas Pallete},
  journal={Bulletin of the London Mathematical Society},
  year={2022},
  volume={54}
}
Let M$M$ be a hyperbolic 3‐manifold with no rank two cusps admitting an embedding in S3$\mathbb {S}^3$ . Then, if M$M$ admits an exhaustion by π1$\pi _1$ ‐injective sub‐manifolds there exists Cantor sets Cn⊆S3$C_n\subseteq \mathbb {S}^3$ such that Nn=S3∖Cn$N_n=\mathbb {S}^3\setminus C_n$ is hyperbolic and Nn→M$N_n\rightarrow M$ geometrically. 

Effective contraction of skinning maps

. Using elementary hyperbolic geometry, we give an explicit for-mula for the contraction constant of the skinning map over moduli spaces of relatively acylindrical hyperbolic manifolds.

References

SHOWING 1-10 OF 49 REFERENCES

Hyperbolization of infinite-type 3-manifolds

We study the class $\mathcal M^B$ of 3-manifolds $M$ that have a compact exhaustion $M=\cup_{i\in\mathbb N} M_i$ satisfying: each $M_i$ is hyperbolizable with incompressible boundary and each

Algebraic and topological properties of big mapping class groups

Let $S$ be an orientable, connected surface with infinitely-generated fundamental group. The main theorem states that if the genus of $S$ is finite and at least 4, then the isomorphism type of the

Geometric limits of knot complements

We prove that any complete hyperbolic 3‐manifold with finitely generated fundamental group, with a single topological end, and which embeds into S3 is the geometric limit of a sequence of hyperbolic

Gromov-Hyperbolicity of the ray graph and quasimorphisms on a big mapping class group

These notes are the English version of the paper "Hyperbolicit\'e du graphe des rayons et quasi-morphismes sur un gros groupe modulaire". The mapping class group Gamma of the complement of a Cantor

Tameness of hyperbolic 3-manifolds

We show that hyperbolic 3-manifolds with finitely generated fundamental group are tame, that is the ends are products. We actually work in slightly greater generality with pinched negatively curved

Existence of ruled wrappings in hyperbolic 3-manifolds

We present a short elementary proof of an existence theorem of certain CAT. 1/‐ surfaces in open hyperbolic 3‐manifolds. The main construction lemma in Calegari and Gabai’s proof of Marden’s Tameness

On 3-manifolds

  • S. Nikitin
  • Mathematics
    Graduate Studies in Mathematics
  • 2021
It is well known that a three dimensional (closed, connected and compact) manifold is obtained by identifying boundary faces from a polyhedron P. The study of (\partial P)/~, the boundary \partial P

A locally hyperbolic 3-manifold that is not homotopy equivalent to any hyperbolic 3-manifold

We construct a locally hyperbolic 3-manifold $M$ such that $\pi_ 1(M)$ has no divisible subgroups. We then show that $M$ is not homotopy equivalent to any complete hyperbolic manifold.

Geometry and Topology of 3-manifolds

Low-dimensional topology is an extremely rich eld of study, with many dierent and interesting aspects. The aim of this project was to expand upon work previously done by I. R. Aitchison and J.H.

Homotopy equivalences of 3-manifolds and deformation theory of Kleinian groups

Introduction Johannson's characteristic submanifold theory Relative compression bodies and cores Homotopy types Pared 3-manifolds Small 3-manifolds Geometrically finite hyperbolic 3-manifolds