8 citations · 21 across the 12 of their papers we have counts for
13 papers
Knot exteriors with all compact surfaces of positive genus essentially embedded
Joao M. Nogueira
It is well known that there exist knots with Seifert surfaces of arbitrarily high genus. In this paper, we show the existence of infinitely many knot exteriors where each of which…
On embeddings of -string tangles into the unknot, the unlink and split links
João M. Nogueira, António Salgueiro
In this paper we study further when tangles embed into the unknot, the unlink or a split link. In particular, we study obstructions to these properties through geometric characteri…
Infinitely many meridional essential surfaces of bounded genus in hyperbolic knot exteriors
João Miguel Nogueira
We show the existence of an infinite collection of hyperbolic knots where each of which has in its exterior meridional essential planar surfaces of arbitrarily large number of boun…
On unknotting tunnel systems of satellite chain links
Darlan Girão, João M. Nogueira, António Salgueiro
We prove that the tunnel number of a satellite chain link with a number of components higher than or equal to twice the bridge number of the companion is as small as possible among…
Cycle convexity and the tunnel number of links
Júlio Araújo, Victor Campos, Darlan Girão +3
In this work, we introduce a new graph convexity, that we call Cycle Convexity, motivated by related notions in Knot Theory. For a graph , define the interval function in…
On links minimizing the tunnel number
Darlan Girão, João M. Nogueira, António Salgueiro
We show a combinatorial argument in the diagram of large class of links, including satellite and hyperbolic links, where for each of which the tunnel number is the minimum possible…
Knot exteriors with all possible meridional essential surfaces
João M. Nogueira
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, t…
Prime knot complements with meridional essential surfaces of arbitrarily high genus
João Miguel Nogueira
We show the existence of infinitely many prime knots each of which having in their complements meridional essential surfaces with two boundary components and arbitrarily high genus…
The number of strings on essential tangle decompositions of a knot can be unbounded
João Miguel Nogueira
We construct an infinite collection of knots with the property that any knot in this family has -string essential tangle decompositions for arbitrarily high .
Fiber surfaces from alternating states
Darlan Girão, João M. Nogueira, António Salgueiro
In this paper we define alternating Kauffman states of links and we characterize when the induced state surface is a fiber. In addition, we give a different proof of a similar theo…
The minimum crossing number of essential tangles
João Miguel Nogueira, António Salgueiro
In this paper we compute the sharp lower bounds for the crossing number of -string -loop essential tangles. For essential tangles with only string components, we characterise…
Tunnel number degeneration under the connected sum of prime knots
João Miguel Nogueira
We study 2-string free tangle decompositions of knots with tunnel number two. As an application, we construct infinitely many counter-examples to a conjecture in the literature sta…
Incompressible surfaces in handlebodies and boundary reducible 3-manifolds
João Miguel Nogueira, Henry Segerman
We study the existence of incompressible embeddings of surfaces into the genus two handlebody. We show that for every compact surface with boundary, orientable or not, there is an…