8 citations · 11 across the 16 of their papers we have counts for
17 papers
Every Link Has Infinitely Many Explicit Generalised T-Link Presentations
Thiago de Paiva, Yi Liu
Generalised -links provide a simple description of all links in as closures of products of standard twisting blocks, parametrised by finite sequences of integers. We prove…
The Lorenz braid index and hyperbolic volume
Thiago de Paiva, Connie On Yu Hui, José Andrés Rodríguez Migueles
A result of Futer, Kalfagianni, and Purcell implies that an upper volume bound for all link complements in the 3-sphere cannot depend solely on the braid index. In this paper, we i…
Lorenz Links that are not Horseshoe and Rossler Links
Thiago de Paiva, Yi Liu
We compare the periodic orbit types of the Lorenz, horseshoe, and Rössler systems through their associated templates. Lorenz links are carried by the Lorenz template, while horsesh…
Satellite Links with Multiple Full Twists and Single-Twist Companions
Thiago de Paiva, Yi Liu, Paolo Piccione
We study the relationship between the number of full twists in positive braid representations of satellite links and their companion links. We construct infinitely many satellite l…
Essential tori associated with links of mixed singularities
Raimundo N. Araújo dos Santos, Benjamin Bode, Thiago de Paiva +1
We establish a direct connection between the analytic data of weakly isolated mixed singularities and the topology of their associated links. More precisely, we prove that the exis…
Generalised T-links Represent All Links in the 3-Sphere
Thiago de Paiva, Connie On Yu Hui, José Andrés Rodríguez Migueles
We introduce generalised T-links, a restricted extension of the widely studied families of T-links and twisted torus links, and prove that this family is universal: every link in t…
Lorenz links, T-links, Minimal Braids, Positive braids with a full twist, and Geometric Types
Thiago de Paiva
Lorenz links and T-links are equivalent families by the work of Birman--Kofman. Lorenz links arise as periodic orbits of the Lorenz system, whereas T-links are closures of certain…
Geometry of Generalized Augmented Braids
Thiago de Paiva
A generalized augmented link of a knot is a link obtained by adding trivial components to that bound -punctured disks. In this paper we consider that is given by a p…
Crushing Surfaces of Positive Genus
Benjamin A. Burton, Thiago de Paiva, Alexander He +1
The operation of crushing a normal surface has proven to be a powerful tool in computational -manifold topology, with applications both to triangulation complexity and to algori…
The New Small Wheel electronics
G. Iakovidis, L. Levinson, Y. Afik +99
The increase in luminosity, and consequent higher backgrounds, of the LHC upgrades require improved rejection of fake tracks in the forward region of the ATLAS Muon Spectrometer. T…
Hyperbolic and satellite Lorenz links obtained by twisting
Thiago de Paiva, Jessica S. Purcell
A Lorenz link is equivalent to a T-link, which is a positive braid built by concatenating torus braids of increasing size. When each torus braid except the largest is obtained by f…
Satellite knots that cannot be represented by positive braids with full twists
Thiago de Paiva
A positive braid with at least one full twist is known to be a minimal braid, i.e, it achieves the braid index for its closure. In this paper we find knots that are the closure of…
Torus Lorenz Links obtained by Full Twists along Torus Links
Thiago de Paiva
All knots are known to be hyperbolic, satellite, or torus knots, and one important family is Lorenz links, or T-links, which arise from dynamics. However, it remains difficult to d…
Hyperbolic Twisted Torus Links
Thiago de Paiva
The twisted torus link is obtained by twisting parallel strands of the -torus link a total of full times. In this paper we find all twisted torus li…
Hyperbolic Knots given by Positive Braids with at Least two Full Twists
Thiago de Paiva
We give some conditions on positive braids with at least two full twists that ensure their closure is a hyperbolic knot, with applications to the geometric classification of T-link…
Satellites and Lorenz knots
Thiago de Paiva, Jessica S. Purcell
We construct infinitely many families of Lorenz knots that are satellites but not cables, giving counterexamples to a conjecture attributed to Morton. We amend the conjecture to st…
Unexpected Essential Surfaces among Exteriors of Twisted Torus Knots
Thiago de Paiva
The twisted torus knots K(p, q; r, s) are obtained by performing a sequence of s full twists on r adjacent strands of (p, q)-torus knots. Morimoto asked whether all twisted torus k…