arXiv research

Generators of the 4-sphere's smooth mapping class group via diffeomorphisms of Montesinos twins.

New findings about twists in 4-sphere diffeomorphisms.

C. Giller proposed an invariant of ribbon 2-knots in S^4 based on a type of skein relation for a projection to R^3. In certain cases, this invariant is equal to the Alexander polynomial for the 2-knot. Giller's invariant is, however, a symmetric polynomial -- which the Alexander polynomial of a 2-knot need not be. Afte…

We classify the Montesinos links up to mutation and 5-move equivalence, and obtain from this a Jones and Kauffman polynomial test for a Montesinos link.

The study proves large alternating Montesinos knots cannot have purely cosmetic surgeries.

We construct an infinite family of quasi-alternating links from a given quasi-alternating link by replacing a crossing by a product of rational tangles each of which extends that crossing. Consequently, we determine an infinite family of quasi-alternating Montesinos links. This family contains all the classes of quasi-…

Exceptional Dehn surgeries have been classified for 2-bridge knots and Montesinos knots of length at least 4. In this paper we classify all toroidal Dehn surgeries on Montesinos knots of length 3.

Study calculates twisted Alexander polynomials for Montesinos knots.

In this note, we complete the classification of quasi-alternating Montesinos links. We show that the quasi-alternating Montesinos links are precisely those identified independently by Qazaqzeh-Chbili-Qublan and Champanerkar-Ording. A consequence of our proof is that a Montesinos link $L$ is quasi-alternating if and onl…

This paper explores Brunnian twin groups and their properties.

We show that the volume of any Montesinos link can be bounded above and below in terms of the combinatorics of its diagram. This was known for Montesinos links with at most two tangles, and those with at least five tangles. We complete the result for the remaining cases.

Using Hirasawa-Murasugi's classification of fibered Montesinos knots we classify the L-space Montesinos knots, providing further evidence towards a conjecture of Lidman-Moore that L-space knots have no essential Conway spheres. In the process, we classify the fibered Montesinos knots whose open books support the tight …

In this paper we show that Montesinos links of the form L(1/2, 1/2, p/q;e), which we call (2,2,r)-Montesinos links, have finite involutory quandles. This generalizes an observation of Winker regarding the (2, 2, q)-pretzel links. We also describe some properties of these quandles.

Twinning splits data into fast, statistically similar sets.

Study on twin groups with algorithm and properties.

We find two new classes of virtually fibered classic Montesinos links of type $\widetilde{SL_2}$.

We give a complete classification of the Dehn surgeries on Montesinos knots which yield manifolds with cyclic or finite fundamental groups.

We will use immersed surfaces to study Seifert fibered surgery on Montesinos knots, and show that if $\frac 1{q_1-1} + \frac 1{q_2-1} + \frac 1{q_3-1} \leq 1$ then a Montesinos knot $K(\frac{p_1}{q_1}, \frac{p_2}{q_2}, \frac{p_3}{q_3})$ admits no atoroidal Seifert fibered surgery.

The paper introduces twins in Kähler and Sasaki geometry, generalizing known concepts.

We report some minimal surfaces that can be seen as copies of a triply periodic minimal surface (TPMS) related by reflections in parallel mirrors. We call them minimal twin surfaces for the resemblance with twin crystal. Brakke's Surface Evolver is employed to construct twinnings of various classical TPMS, including Sc…

Proves a property of certain 3D knots and links.

Paper finds linking numbers for Montesinos links using a simple algorithm.

New method for simplifying knots with specific properties.

This note corrects errors in Hatcher and Oertel's table of boundary slopes of Montesinos knots which have projections with 10 or fewer crossings.

We find a larger class of virtually fibred classic Montesinos links of type $\widetilde{SL_2}$, extending a result of Agol, Boyer and Zhang.

Improved aircraft structure prediction using derivative-enhanced sparse Cholesky GP method.

We establish the slice-ribbon conjecture for a large family of Montesinos' knots by means of Donaldson's theorem on the intersection forms of definite 4-manifolds.

Virtual twin groups map to symmetric groups, revealing automorphism structure.

Generative models create personalized patient health simulations.

Quasi-alternating links are a generalization of alternating links. They are homologically thin for both Khovanov homology and knot Floer homology. Recent work of Greene and joint work of the first author with Kofman resulted in the classification of quasi-alternating pretzel links in terms of their integer tassel param…

We show that if a Montesinos knot admits a Dehn surgery yielding a toroidal Seifert fibered 3-manifold, then the knot is the trefoil knot and the surgery slope is 0.

It is shown that the diameter of the boundary slope set is bounded from above by the twice of the minimal crossing number for a Montesinos knot.

We give (1) an upper bound on the denominators of numerical boundary slopes and (2) an upper bound on the differences between two numerical boundary slopes, for Montesinos knot exteriors.

The paper shows some Montesinos links can't be doubly sliced strongly.

Surrogate models enhance digital twin technology for dynamic systems.

Study counts specific surfaces in Montesinos knots with 4 rational tangles.

fMRI is a unique non-invasive approach for understanding the functional organization of the human brain, and task-based fMRI promotes identification of functionally relevant brain regions associated with a given task. Here, we use fMRI (using the Poffenberger Paradigm) data collected in mono- and dizygotic twin pairs t…

Smooth manifolds can be triangulated with graphs of bounded twin-width.

A filling Dehn sphere $Σ$ in a closed 3-manifold $M$ is a sphere transversely immersed in $M$ that defines a cell decomposition of $M$. Every closed 3-manifold has a filling Dehn sphere. The Montesinos complexity of a $3$-manifold $M$ is defined as the minimal number of triple points among all the filling Dehn spheres …

It is shown that there exist alternating non-Montesinos knots whose essential spanning surfaces with maximal and minimal boundary slopes are not realised by the checkerboard surfaces coming from a reduced alternating planar diagram.

Study shows torsion in knot module for specific Montesinos knots.

Digital twin reduces costs in various fields.

Paper studies pure virtual twin groups and their automorphisms.

Method determines SL(2,C) character variety for Montesinos knots.

Proposes a probabilistic digital twin for dynamical systems using sparse Bayesian learning.

Deep RL optimizes sensor placement in digital twins for dynamic data acquisition.

The (Strong) Slope Conjecture relates the degree of the colored Jones polynomial of a knot to certain essential surfaces in the knot complement. We verify the Slope Conjecture and the Strong Slope Conjecture for 3-string Montesinos knots satisfying certain conditions.

A ravel is a spatial graph which is non-planar but contains no non-trivial knots or links. We characterize when a Montesinos tangle can become a ravel as the result of vertex closure with and without replacing some number of crossings by vertices.