arXiv research

We discuss $SU(2)$ Bogomolny monopoles of arbitrary charge $k$ invariant under various symmetry groups. The analysis is largely in terms of the spectral curves, the rational maps, and the Nahm equations associated with monopoles. We consider monopoles invariant under inversion in a plane, monopoles with cyclic symmetry…

The study connects monopole chains to Higgs bundles and classifies symmetric chains.

Study on JNR monopoles, focusing on their spectral curves and energy density.

Study of large mass limits of G2 and Calabi-Yau monopoles on specific manifolds.

Researchers found examples of $G_2$-monopoles with singularities.

We define and study certain hyperkaehler manifolds which capture the asymptotic behaviour of the SU(2)-monopole metric in regions where monopoles break down into monopoles of lower charges. The rate at which these new metrics approximate the monopole metric is exponential, as for the Gibbons-Manton metric.

We discuss the spectral curves and rational maps associated with $SU(2)$ Bogomolny monopoles of arbitrary charge $k$. We describe the effect on the rational maps of inverting monopoles in the plane with respect to which the rational maps are defined, and discuss the monopoles invariant under such inversion. We define t…

We classify hyperbolic monopoles with continuous symmetries and construct new examples.

Study shows instantons and monopoles decompose into U(1) components.

Study periodic monopoles via algebraic difference modules.

Study contact structures and sutured monopole Floer homology, computing and deriving formulas.

Paper constructs maps for sutured monopole Floer homology.

Researchers create BPS monopoles with any desired symmetry breaking.

Classifies charge-3 monopoles with symmetry, identifying new spectral curves.

Proves a new skein exact triangle for real monopole Floer homology.

Study finds a specific submanifold in monopole moduli space.

Develops twistorial approach to define monopoles on R^5.

Researchers compactify magnetic monopole moduli spaces, revealing new metric properties.

Existence of non-trivial monopoles on 3-spheres proven.

New gauge condition fixes $L^2$ metric divergence in hyperbolic monopole spaces.

Abstract relates G2 instantons to Seiberg-Witten monopoles.

Compactifies SU(2) monopole moduli spaces, proving part of Sen's conjecture.

$G_2$-Monopoles are solutions to gauge theoretical equations on noncompact $7$-manifolds of $G_2$ holonomy. We shall study this equation on the $3$ Bryant-Salamon manifolds. We construct examples of $G_2$-monopoles on two of these manifolds, namely the total space of the bundle of anti-self-dual two forms over the $\ma…

We show that many hyperbolic monopoles can be distinguished from each other via their asymptotic values in contrast to the case of Euclidean monopoles.

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 singularities. We present an alternative construction of singular monopoles formulated i…

Develops invariants for webs and foams using Seiberg-Witten theory.

We associate to an SU(2) hyperbolic monopole a holomorphic sphere embedded in projective space and use this to uncover various features of the monopole.

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 charge and arbitrary mass. Previously, aside from charge one monopoles, existenc…

Study monopole h-invariants from a topological viewpoint.

Monopole dynamics linked to crystal volumes via moduli space geometry.

We construct periodic monopoles (with singularities), i.e. monopoles on $\mathbb{R}^{2} \times \mathbb{S}^{1}$ possibly singular at a finite collection of points, by gluing methods.

Study on monopoles with singularities on 3-folds, proving Fredholmness and calculating $L^2$-indices.

Derives a formula for fermion dimensions in spherically symmetric monopole backgrounds.

In this expository review we discuss various aspects of gauge theory. While the focus is on mathematics, wherever possible we make contact with theoretical high energy physics. Particular emphasis is placed on instantons and monopoles, which admit physical interpretation, and yield interesting and nontrivial mathematic…

The study examines sequences of 3D generalised monopoles with uniform bounds.

Explains connections between monopoles and modules on elliptic curves.

Local solutions to $G_{2}$-monopole equations exist for any locally defined structures.

We construct monopoles in any asymptotically conical (AC) $3$-manifold $X$ with $b^2(X)=0$. For sufficiently large mass, our construction covers an open set in the moduli space of monopoles. We also give a more general construction of Dirac monopoles in any AC manifold, which may be useful for generalizing our result t…

Study on large mass monopoles focusing on their limiting behavior and properties.

We construct the first nontrivial examples of Calabi-Yau monopoles. Our main interest on these, comes from Donaldson and Segal's suggestion \cite{Donaldson2009} that it may be possible to define an invariant of certain noncompact Calabi-Yau manifolds from these gauge theoretical equations. We focus on the Stenzel metri…

Study of Haydys monopoles using complexified Bogomolny equations.

A quasiclassical method approximates magnetic monopole eigenvalues.

Transforms instantons to monopoles for torus products.

Study of supersymmetric deformations and monopoles in Kahler geometry.

Study of continuous symmetries in Nahm data and BPS monopoles.

Study of Pin(2)-monopole Floer homology under connected sums.

The study examines asymptotic properties of G2-monopoles on nonparabolic G2-manifolds.

Study SO(3) vortices over orbifold Riemann surfaces and monopoles.