Related papers: A gluing construction for periodic monopoles
We show that for generic choices of parameters the moduli spaces of periodic monopoles (with singularities), i.e. monopoles on $\mathbb{R}^{2} \times \mathbb{S}^{1}$ possibly singular at a finite collection of points, are either empty or…
$G_2$-monopoles are solutions to gauge theoretical equations on $G_2$-manifolds. If the $G_2$-manifolds under consideration are compact, then any irreducible $G_2$-monopole must have singularities. It is then important to understand which…
We establish a canonical gluing procedure for Seiberg-Witten monopoles on the two pieces of a closed, oriented 4-manifold X which is split along a 3-dimensional closed, oriented submanifold. We only assume that the (unperturbed) character…
We study periodic monopoles satisfying some mild conditions, called of GCK type. Particularly, we give a classification of periodic monopoles of GCK type in terms of difference modules with parabolic structure, which is a kind of…
Gluing is a cut and paste construction where the dynamics of a map in a given domain is replaced by a different one, under the condition that the two agree along the gluing curve. Here we consider two polynomials with a finite…
We construct a model in which stable magnetic monopoles have magnetic charges that are identical to the electric charges on leptons and quarks and the colored monopoles are confined by strings in color singlets.
Singular monopoles are nonabelian monopoles with prescribed Dirac-type singularities. All of them are delivered by the Nahm's construction. In practice, however, the effectiveness of the latter is limited to the cases of one or two…
We propose a method to create a monopole structure in a spin-1 spinor condensate by applying the basic methods used to create vortices and solitons experimentally in single-component condensates. We show, however, that by using a…
`Gluing' is a technique of constructing solutions to non-linear (elliptic) partial differential equations such as Yang--Mills equations, minimal surface equations and Einstein equations. Calibrated submanifolds are a certain class of…
There are three types of monopole in gauge theories with fundamental matter and N=2 supersymmetry broken by a superpotential. There are unconfined 0-monopoles and also 1 and 2-monopoles confined respectively by one or two vortices…
We discuss some properties of the abelian monopoles in compact U(1) gauge theory and in the SU(2) gluodynamics both on the lattice and in the continuum.
On a complete manifold, such as Euclidean 3-space or hyperbolic 3-space, the limit at infinity of the norm of the Higgs field is called the mass of the monopole. We show the existence, on hypebolic 3-space, of monopoles with given magnetic…
We describe a physical mechanism for creating multi-soliton bound states where solitons are glued together by attraction between the beams they guide, `solitonic gluons'. We verify the concept of the solitonic gluons experimentally,…
We provide a framework to classify hyperbolic monopoles with continuous symmetries and find a Structure Theorem, greatly simplifying the construction of all those with spherically symmetry. In doing so, we reduce the problem of finding…
We prove the existence of non-trivial irreducible SU(2)-monopoles with Dirac singularities on any rational homology 3-sphere, equipped with any Riemannian metric, using a gluing construction.
Given a $\mathbb Z_2$-harmonic spinor satisfying some genericity assumptions, this article constructs a 1-parameter family of two-spinor Seiberg-Witten monopoles converging to it after renormalization. The proof is a gluing construction…
We consider geometrical characteristics of monopole clusters of the lattice SU(2) gluodynamics. We argue that the polymer approach to the field theory is an adequate means to describe the monopole clusters. Both finite-size and the…
Motivated by recent results on small and hollow magnetic monopoles and on core and shell bimagnetic nanoparticles, we propose the construction of bimagnetic monopoles, which are structures that accommodate a magnetic monopole inside another…
A finitely generated commutative monoid is uniquely presented if it has only a minimal presentation. We give necessary and sufficient conditions for finitely generated, combinatorially finite, cancellative, commutative monoids to be…
In this paper we construct gluing maps and cobordism maps for sutured monopole Floer homology.