Related papers: Persistently laminar branched surfaces

We give a sufficient condition for a branched surface in a 3 dimensional manifold to fully carry a lamination, giving a piece of answer to a classical question of D. Gabai.

We introduce and analyze the characteristic foliation induced by a contact structure on a branched surface, in particular a branched standard spine of a 3-manifold. We extend to (fairly general) singular foliations of branched surfaces the…

We show that quasi-alternating links arise naturally when considering surgery on a strongly invertible L-space knot (that is, a knot that yields an L-space for some Dehn surgery). In particular, we show that for many known classes of…

We show the existence of infinitely many knot exteriors where each of which contains meridional essential surfaces of any genus and (even) number of boundary components. That is, the compact surfaces that have a meridional essential…

It is shown that given any link-manifold, there is an algorithm to decide if the manifold contains an embedded, essential planar surface; if it does, the algorithm will construct one. If a slope on the boundary of the link-manifold is…

We show that every nonzero integer occurs in the denominator of a boundary slope for infinitely many (1,1)-knots and that infinitely many (1,1)-knots have boundary slopes of arbitrarily small difference. Specifically, we prove that for any…

We introduce veering branched surfaces as a dual way of studying veering triangulations. We then discuss some surgical operations on veering branched surfaces. Using these, we provide explicit constructions of some veering branched surfaces…

In the complement of a hyperbolic Montesinos knot with 4 rational tangles, we investigate the number of closed, connected, essential, orientable surfaces of a fixed genus $g$, up to isotopy. We show that there are exactly 12 genus 2…

Let K be a tame knot with irreducible exterior M(K) in a closed, connected, orientable 3--manifold Sigma such that pi_1(Sigma) is cyclic. If infinity is not a strict boundary slope, then the diameter of the set of strict boundary slopes of…

A branched covering surface-knot over an oriented surface-knot $F$ is a surface-knot in the form of a branched covering over $F$. A branched covering surface-knot over $F$ is presented by a graph called a chart on a surface diagram of $F$.…

We give an algorithm for a surgery description of a $p$-fold cyclic branched cover of $B^3$ branched along a tangle. We generalize constructions of Montesinos and Akbulut-Kirby.

We show that if a knot or link has n thin levels when put in thin position then its exterior contains a collection of n disjoint, non-parallel, planar, meridional, essential surfaces. A corollary is that there are at least n/3 tetrahedra in…

Strongly-cyclic branched coverings of knots are studied by using their (g,1)-decompositions. Necessary and sufficient conditions for the existence and uniqueness of such coverings are obtained. It is also shown that their fundamental groups…

There are examples of branched surfaces that do not fully carry laminations, but their preimage in a finite cover does fully carry a lamination

Given $I,B\in\mathbb{N}\cup \{0\}$, we investigate the existence and geometry of complete finitely branched minimal surfaces $M$ in $\mathbb{R}^3$ with Morse index at most $I$ and total branching order at most $B$. Previous works of…

Let $K\subseteq S^3$ be a knot with exterior $E_K$, and denote by $\rho\colon \pi_1(E_K)\twoheadrightarrow G$ a quotient of its group. We give a sharp obstruction to the existence of a connected, oriented, smooth surface $F\subseteq B^4$…

Suppose $K$ is a hyperbolic knot in a solid torus $V$ intersecting a meridian disk $D$ twice. We will show that if $K$ is not the Whitehead knot and the frontier of a regular neighborhood of $K \cup D$ is incompressible in the knot…

The knot group is the fundamental group of a knot or link complement. A necessary and sufficient conditions for a group to be realized as the knot group of some link was provided. This result was shown using the closed braid method.…

Racks do not give us invariants of surface-knots in general. For example, if a surface-knot diagram has branch points (and a rack which we use satisfies some mild condition), then it admits no rack colorings. In this paper, we investigate…

Let $M$ be a closed hyperbolic 3-manifold with a fibered face $\sigma$ of the unit ball of the Thurston norm on $H_2(M)$. If $M$ satisfies a certain condition related to Agol's veering triangulations, we construct a taut branched surface in…