Related papers: Filling Links and Essential Systole

We introduce and study the notion of filling links in 3-manifolds: a link L is filling in M if for any 1-spine G of M which is disjoint from L, $\pi_1(G)$ injects into $\pi_1(M\smallsetminus L)$. A weaker "k-filling" version concerns…

M. Freedman and V. Krushkal introduced the notion of a "filling" link in a 3-manifold: a link $L$ is filling in $M$ if for any spine $G$ of $M$ disjoint from $L$, $\pi_1(G)$ injects into $\pi_1(M \setminus L )$. Freedman and Krushkal show…

Classical fully augmented links have explicit hyperbolic geometry, and have diagrams on the 2-sphere in the 3-sphere. We generalise to construct fully augmented links projected to the reflection surface of any 3-manifold obtained by…

In the first part of this paper, we construct infinitely many hyperbolic closed 3-manifolds which admit no symplectic fillable contact structure. All these 3-manifolds are obtained by Dehn surgeries along L-space knots or L-space…

Menasco proved that nontrivial links in the 3-sphere with connected prime alternating non-2-braid projections are hyperbolic. This was further extended to augmented alternating links wherein non-isotopic trivial components bounding disks…

It is conjectured that every cusped hyperbolic 3-manifold has a decomposition into positive volume ideal hyperbolic tetrahedra (a "geometric" triangulation of the manifold). Under a mild homology assumption on the manifold we construct…

It has been known for several decades that classical alternating links in the 3-sphere have nice hyperbolic geometric properties. Recent work generalises such results to give hyperbolic geometry of links with alternating projections onto…

We study the systole of a model of random hyperbolic 3-manifolds introduced by Petri and Raimbault, answering a question posed in that same article. These are compact manifolds with boundary constructed by randomly gluing truncated…

We view closed orientable 3-manifolds as covers of S^3 branched over hyperbolic links. For a p-fold cover M \to S^3, branched over a hyperbolic link L, we assign the complexity p Vol(S^3 minus L) (where Vol is the hyperbolic volume). We…

Menasco showed that a non-split, prime, alternating link that is not a 2-braid is hyperbolic in $S^3$. We prove a similar result for links in closed thickened surfaces $S \times I$. We define a link to be fully alternating if it has an…

We prove that for any V>0, there exist a hyperbolic manifold M_V, so that Vol(M_V) < 2.03 and LinVol(M_V) > V. The proof requires study of cosmetic surgery on links (equivalently, fillings of manifolds with boundary tori). There is no bound…

The work of Jorgensen and Thurston shows that there is a finite number N(v) of orientable hyperbolic 3-manifolds with any given volume v. We show that there is an infinite sequence of closed orientable hyperbolic 3-manifolds, obtained by…

A finite-volume hyperbolic 3-manifold geometrically bounds if it is the geodesic boundary of a finite-volume hyperbolic 4-manifold. We construct here an example of non-compact, finite-volume hyperbolic 3-manifold that geometrically bounds.…

We show that the hyperbolic structure on a closed, orientable, hyperbolic 3-manifold can be constructed from a solution to the hyperbolic gluing equations using any triangulation with essential edges. The key ingredients in the proof are…

In this paper, we find infinite hyperbolic 3-manifolds that admit no weakly symplectically fillable contact structures, using tools in Heegaard Floer theory. We also remark that part of these manifolds do admit tight contact structures.

In this paper we study the systoles of arithmetic hyperbolic 2- and 3-manifolds. Our first result is the construction of infinitely many arithmetic hyperbolic 2- and 3-manifolds which are pairwise noncommensurable, all have the same…

Let N be a topologically finite, orientable 3-manifold with ideal triangulation. We show that if there is a solution to the hyperbolic gluing equations, then all edges in the triangulation are essential. This result is extended to a…

In arxiv:1205.1274 Rieck and Yamashita defined the link volume of 3-manifolds and studied some of its basic properties. Many of these properties are similar to the corresponding properties of the hyperbolic volume. In this paper we…

Given a link in a 3-manifold such that the complement is hyperbolic, we provide two modifications to the link, called the chain move and the switch move, that preserve hyperbolicity of the complement, with only a relatively small number of…

In this article, for any $n\geq 4$ we construct a sequence of compact hyperbolic $n$-manifolds $\{M_i\}$ with number of systoles at least as $\mathrm{vol}(M_i)^{1+\frac{1}{3n(n+1)}-\epsilon}$ for any $\epsilon>0$. In dimension 3, the bound…