Related papers: Excluding cosmetic surgeries on hyperbolic 3-manif…

We give an upper bound on the distance between a degeneracy slope for a very full essential lamination and a boundary slope of an essential surface embedded in a compact, orientable, irreducible, atoroidal 3-manifold with incompressible…

In this paper, we show that any non-arithmetic hyperbolic $2$-bridge link complement admits no hidden symmetries. As a corollary, we conclude that a hyperbolic $2$-bridge link complement cannot irregularly cover a hyperbolic $3$-manifold.…

In this paper we clarify an issue in the knot surgery construction of Fintushel and Stern. Using knot surgery, they construct an infinite number of smooth structures on 4-manifolds satisfying certain conditions, but they do not explicitly…

In Dunfield's catalog of the hyperbolic manifolds in the SnapPy census which are complements of L-space knots in $S^3$, we determine that $22$ have tunnel number $2$ while the remaining all have tunnel number $1$. Notably, these $22$…

Finite-order invariants of knots in arbitrary 3-manifolds (including non-orientable ones) are constructed and studied by methods of the topology of discriminant sets. Obstructions to the integrability of admissible weight systems to…

Given a knot K in the three-sphere, we address the question: which Dehn surgeries on K bound negative-definite four-manifolds? We show that the answer depends on a number m(K), which is a smooth concordance invariant. We study the…

We present a new, practical algorithm to test whether a knot complement contains a closed essential surface. This property has important theoretical and algorithmic consequences; however, systematically testing it has until now been…

Which slopes can or cannot appear as Seifert fibered slopes for hyperbolic knots in the 3-sphere S^3? It is conjectured that if r-surgery on a hyperbolic knot in S^3 yields a Seifert fiber space, then r is an integer. We show that for each…

We have developed a reinforcement learning agent that often finds a minimal sequence of unknotting crossing changes for a knot diagram with up to 200 crossings, hence giving an upper bound on the unknotting number. We have used this to…

Suppose F is a compact orientable surface, K is a knot in F x I, and N is the 3-manifold obtained by some non-trivial surgery on K. If F x {0} compresses in N, then there is an annulus in F x I with one end K and the other end an essential…

This paper gives a proof that the fundamental group of a class of closed orientable 3-manifolds constructed from three injective handlebodies has a solvable word problem. This is done by giving an algorithm to decide if a closed curve in…

We prove that all knots with unknotting number at most 21 are smoothly slice in the K3 surface. We also prove a more general statement for 4-manifolds that contain a plumbing tree of spheres. Our strategy is based on a flexible method to…

A triple crossing is a crossing in a projection of a knot or link that has three strands of the knot passing straight through it. A triple crossing projection is a projection such that all of the crossings are triple crossings. We prove…

Motivated by a question of Neumann and Reid, we study whether Dehn fillings on all but one cusp of a hyperbolic link complement can produce infinite families of knot complements with hidden symmetries which geometrically converge to the…

We present a combinatorial approach to the existence of foliations and contact structures transverse to a given pseudo-Anosov flow. Let $\varphi$ be a transitive pseudo-Anosov flow on a closed oriented 3-manifold. Our main technical result…

We propose a new algorithm for Dehn surgery problem, finding exceptional Dehn filling slopes for a given hyperbolic 3-manifold with a torus boundary, using a quantum invariant called "3D index". The invariant is defined using an ideal…

We examine the structure and dimensionality of the Jones polynomial using manifold learning techniques. Our data set consists of more than 10 million knots up to 17 crossings and two other special families up to 2001 crossings. We introduce…

For any hyperbolic genus one 2-bridge knot in the 3-sphere, we show that the resulting manifold by $r$-surgery on the knot has left-orderable fundamental group if the slope $r$ lies in some range which depends on the knot.

We consider the question of when the operation of contact surgery with positive surgery coefficient, along a knot $K$ in a contact 3-manifold $Y$, gives rise to a weakly fillable contact structure. We show that this happens if and only if…

For every $k \geq 2$ we construct infinitely many $4k$-dimensional manifolds that are all stably diffeomorphic but pairwise not homotopy equivalent. Each of these manifolds has hyperbolic intersection form and is stably parallelisable. In…