相关论文: Hyperbolic L-space knots not concordant to algebra…

We show there exist infinitely many knots of every fixed genus $g\geq 2$ which do not admit surgery to an L-space, despite resembling algebraic knots and L-space knots in general: they are algebraically concordant to the torus knot…

The hyperbolic structure on a 3-dimensional cone-manifold with a knot as singularity can often be deformed into a limiting Euclidean structure. In the present paper we show that the respective normalised Euclidean volume is always an…

We give sufficient conditions for a satellite knot to admit an L-space surgery, and use this result to give new infinite families of patterns which produce satellite L-space knots.

For a given knot $K$ and $w>0$, we construct infinitely many mutually distinct hyperbolic knots $\{K_i\}$ such that the $P$-satellites of $K$ and $K_i$ have the same HOMFLY polynomial up to given $z$-degrees, for all braided patterns $P$…

We extend the list of known band structure topologies to include a large family of hyperbolic nodal links and knots, occurring both in conventional Hermitian systems where their stability relies on discrete symmetries, and in the…

We prove that any complete hyperbolic 3--manifold with finitely generated fundamental group, with a single topological end, and which embeds into $\BS^3$ is the geometric limit of a sequence of hyperbolic knot complements in $\BS^3$. In…

Geometrical constraints imposed on higher dimensional harmonic lattices generally lead to nonlinear dynamical lattice models. Helical lattices obtained by such a procedure are shown to be described by sine- plus linear-lattice equations.…

Given a hyperbolic knot $K$ and any $n\geq 2$ the abelian representations and the holonomy representation each give rise to an $(n-1)$-dimensional component in the $\operatorname{SL}(n,\Bbb{C})$-character variety. A component of the…

We prove that if a proper metric space is quasi-isometric to a finitely generated group and to a space with a horoball over a finitely generated group, then that space is quasi-isometric to a rank-one symmetric space or the real line.

We describe four hyperbolic knot complements in $\mathbb{S}^3$, each of which covers a prism orbifold: the quotient of $\mathbb{H}^3$ by the action of a discrete group generated by reflections in the faces of a polyhedron that has the…

We construct compact hyperbolic 3-manifolds with totally geodesic boundary, such that the closed 3-pseudomanifolds obtained by coning off the boundary components are negatively curved and contain locally convex subspaces whose fundamental…

For any H in [0,1), we construct complete, non-proper, stable, simply-connected surfaces with constant mean curvature H embedded in hyperbolic 3-space.

It has been an open question whether all boundary slopes of hyperbolic knots are strongly detected by the character variety. The main result of this paper produces an infinite family of hyperbolic knots each of which has at least one strict…

The first examples of totally geodesic Seifert surfaces are constructed for hyperbolic knots and links, including both free and totally knotted surfaces. Then it is proved that two bridge knot complements cannot contain totally geodesic…

We prove noncoherence of certain families of lattices in the isometry group of the hyperbolic n-space for n greater than 3. For instance, every nonuniform arithmetic lattice in SO(n,1) is noncoherent, provided that n is at least 6.

We show that if $K$ is a nontrivial knot then the proportion of satellites of $K$ among all of the prime non-split links of $n$ or fewer crossings does not converge to $0$ as $n$ approaches infinity. This implies in particular that the…

We construct a hyperbolic 3-manifold $M$ (with $\partial M$ totally geodesic) which contains no essential closed surfaces, but for any even integer $g> 0$ there are infinitely many separating slopes $r$ on $\partial M$ so that $M[r]$, the…

We construct a family of hyperbolic link complements by gluing tangles along totally geodesic four-punctured spheres, then investigate the commensurability relation among its members. Those with different volume are incommensurable,…

We present a statistical approach for the discovery of relationships between mathematical entities that is based on linear regression and deep learning with fully connected artificial neural networks. The strategy is applied to…

We show that given n>0, there exists a hyperbolic knot K with trivial Alexander polynomial, trivial finite type invariants of order <=n, and such that the volume of the complement of K is larger than n. This contrasts with the known…