Related papers: Negative definite spin filling and branched double…
We define a knot invariant and a 2-knot invariant from any finite categorical group. We calculate an explicit example for the Spun Trefoil.
We provide an introduction to the ideas of spin-dependent deep-inelastic scattering. Recent experimental results are summarised and possible explanations related to the axial anomaly presented. Further experiments that could greatly clarify…
In this paper, we use the perspective of linear series, and in particular results following from the degeneration tools of limit linear series, to give a number of new results on existence and non-existence of branched covers of the…
Quandle cocycle invariants form a powerful and well developed tool in knot theory. This paper treats their variations - namely, positive and twisted quandle cocycle invariants, and shadow invariants. We interpret the former as particular…
We use the G-signature theorem to define an invariant of strongly invertible knots analogous to the knot signature.
We show that a finite numerical boundary slope of an essential surface in the exterior of a Montesinos knot is bounded above and below in terms of the numbers of positive/negative crossings of a specific minimal diagram of the knot.
We study knots in $\mathbb{S}^3$ obtained by the intersection of a minimal surface in $\mathbb{R}^4$ with a small 3-sphere centered at a branch point. We construct examples of new minimal knots. In particular we show the existence of…
We prove that a weak Fano manifold has unobstructed deformations. For a general variety, we investigate conditions under which a variety is necessarily obstructed.
We extend the construction of upsilon-type invariants to null-homologous knots in rational homology three-spheres. By considering $m$-fold cyclic branched covers with $m$ a prime power, this extension provides new knot concordance…
An oriented compact 4-manifold $V$ with boundary $S^3$ is called a positon (resp. negaton) if its intersection form is positive definite (resp. negative definite) and it is simply connected. In this paper, we prove that there exist…
We study smooth maps between smooth manifolds with only fold points as their singularities, and clarify the obstructions to the existence of such a map in a given homotopy class for certain dimensions. The obstructions are described in…
The work concerns the quasielastic charged current neutrino-neutron and antineutrino-proton interactions. Single, double, and triple spin asymmetries are computed and analyzed. The spin asymmetries are sensitive to the axial form factor of…
We explore more the properties of bipartite knots and its rich combinatorial structure.
We characterise positive braid links with positive Seifert form via a finite number of forbidden minors. From this we deduce a one-to-one correspondence between prime positive braid links with positive Seifert form and simply laced Dynkin…
A construction of a spatial graph from a strongly invertible knot was developed by the second author, and a necessary and sufficient condition for the given spatial graph to be hyperbolic was provided as well. The condition is improved in…
Weakly generalised alternating knots are knots with an alternating projection onto a closed surface in a compact irreducible 3-manifold, and they share many hyperbolic geometric properties with usual alternating knots. For example, usual…
We investigate the coefficients of the highest and lowest terms (also called the head and the tail) of the colored Jones polynomial and show that they stabilize for alternating links and for adequate links. To do this we apply techniques…
Generalising recent studies on the sawtooth lattice, a two-spin variant of the model is considered. Numerical studies of the energy spectra and the relevant spin correlations in the problem are presented. Perturbation theory analysis of the…
Families of alternating knots (links) and tangles are studied using as building block the conway defined as the twisting of two strands. The regular representation of knots assumes the projection has the minimal number of overpassings, and…
We investigate Kondo effect and spin blockade observed on a many-electron quantum dot and study the magnetic field dependence. At lower fields a pronounced Kondo effect is found which is replaced by spin blockade at higher fields. In an…