A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Constructs an asymptotic metric for moduli space of centred hyperbolic monopoles.
We discuss the spectral curves and rational maps associated with Bogomolny monopoles of arbitrary charge . 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 discuss a 4[k/2]-dimensional complete hyperkähler submanifold of the (4k-4)-dimensional moduli space of strongly centred SU(2)-monopoles of charge k.
We discuss Bogomolny monopoles of arbitrary charge 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…
We develop the Ercolani-Sinha construction of SU(2) monopoles and make this effective for (a five parameter family of centred) charge 3 monopoles. In particular we show how to solve the transcendental constraints arising on the spectral curve. For a class of symmetric curves the transcendental constraints become a numb…
We classify hyperbolic monopoles with continuous symmetries and construct new examples.
New gauge condition fixes metric divergence in hyperbolic monopole spaces.
We show that many hyperbolic monopoles can be distinguished from each other via their asymptotic values in contrast to the case of Euclidean monopoles.
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.
This thesis was motivated by a desire to understand the natural geometry of hyperbolic monopole moduli spaces. We take two approaches. Firstly we develop the twistor theory of singular hyperbolic monopoles and use it to study the geometry of their charge 1 moduli spaces. After this we introduce a new way to study the m…
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…
We discuss the Euclidean limit of hyperbolic SU(2)-monopoles, framed at infinity, from the point of view of pluricomplex geometry. More generally, we discuss the geometry of hypercomplex manifolds arising as limits of pluricomplex manifolds.
We review the theory of JNR, mass 1/2 hyperbolic monopoles in particular their spectral curves and rational maps. These are used to establish conditions for a spectral curve to be the spectral curve of a JNR monopole and to show that that rational map of a JNR monopole monopole arises by scattering using results of Ati…
We prove the conjecture that a monopole in three-dimensional anti-de Sitter space can be completely determined by its ``holographic'' image on the conformal boundary two-sphere.
Classifies charge-3 monopoles with symmetry, identifying new spectral curves.
Gravitational instantons are constructed as superpositions of Atiyah-Hitchin and Taub-NUT geometries.
The classifications of holonomy groups in Lorentzian and in Euclidean signature are quite different. A group of interest in Lorentzian signature in n dimensions is the maximal proper subgroup of the Lorentz group, SIM(n-2). Ricci-flat metrics with SIM(2) holonomy were constructed by Kerr and Goldberg, and a single four…
We determine the group of conformal automorphisms of the self-dual metrics on n#CP^2 due to LeBrun for n>2, and Poon for n=2. These metrics arise from an ansatz involving a circle bundle over hyperbolic three-space H^3 minus a finite number of points, called monopole points. We show that for n>2 connected sums, any con…
The paper studies hyperbolic three-manifolds and their geometric constraints.
Study Floer theory of hyperbolic three-manifolds using Dirac spectral flow.
The discrete Nahm equations, a system of matrix valued difference equations, arose in the work of Braam and Austin on half-integral mass hyperbolic monopoles. We show that the discrete Nahm equations are completely integrable in a natural sense: to any solution we can associate a spectral curve and a holomorphic line-b…
Motivated by strong desire to understand the natural geometry of moduli spaces of hyperbolic monopoles, we introduce and study a new type of geometry: pluricomplex geometry. It is a generalisation of hypercomplex geometry: we still have a 2-sphere of complex structures, but they no longer behave like unit imaginary qua…
We consider the self-dual conformal classes on n#CP^2 discovered by LeBrun. These depend upon a choice of n points in hyperbolic 3-space, called monopole points. We investigate the limiting behavior of various constant scalar curvature metrics in these conformal classes as the points approach each other, or as the poin…
Study Froyshov invariants and closed geodesics in hyperbolic 3-manifolds.
Convexity properties are preserved under radial transformations in hyperbolic and spherical geometries.
We present an algorithm that computes Bowditch's canonical JSJ decomposition of a given one-ended hyperbolic group over its virtually cyclic subgroups. The algorithm works by identifying topological features in the boundary of the group. As a corollary we also show how to compute the JSJ decomposition of such a group o…
We prove that the space of gauge equivalence classes of U(1)-invariant connections on some SU(2)-principle bundles over the 4-sphere S^4 is weakly homotopy equivalent to a component of the second loop space of the 2-sphere S^2.
Develops methods to learn centre groupings from summary statistics in multi-centre studies.
Asymptotics for equidistribution of circles on hyperbolic surfaces.
Groups can be embedded in larger, simpler groups with special properties.
Generalising a seminal result of Epstein and Penner for cusped hyperbolic manifolds, Cooper and Long showed that each decorated strictly convex projective cusped manifold has a canonical cell decomposition. Penner used the former result to describe a natural cell decomposition of decorated Teichmüller space of puncture…
The study connects monopole chains to Higgs bundles and classifies symmetric chains.
Study of large mass limits of G2 and Calabi-Yau monopoles on specific manifolds.
The paper examines the geometry of a curve's centre symmetry set.
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.
The paper classifies discrete complex hyperbolic triangle groups.
Study shows instantons and monopoles decompose into U(1) components.
Expected centre of mass for random embeddings is constant.
-monopoles are solutions to gauge theoretical equations on -manifolds. If the -manifolds under consideration are compact, then any irreducible -monopole must have singularities. It is then important to understand which kind of singularities -monopoles can have. We give examples (in the noncompa…
Researchers create BPS monopoles with any desired symmetry breaking.
We show that the isomorphism problem is solvable in the class of central extensions of word-hyperbolic groups, and that the isomorphism problem for biautomatic groups reduces to that for biautomatic groups with finite centre. We describe an algorithm that, given an arbitrary finite presentation of an automatic group $Γ…
Proves a new skein exact triangle for real monopole Floer homology.
Monotonicity formulae play a crucial role for many geometric PDEs, especially for their regularity theories. For minimal submanifolds in a Euclidean ball, the classical monotonicity formula implies that if such a submanifold passes through the centre of the ball, then its area is at least that of the equatorial disk. R…
In this paper, we explore the interplay between contact structures and sutured monopole Floer homology. First, we study the behavior of contact elements, which were defined by Baldwin and Sivek, under the operation of performing Floer excisions, which was introduced to the context of sutured monopole Floer homology by …
Existence of non-trivial monopoles on 3-spheres proven.
-Monopoles are solutions to gauge theoretical equations on noncompact -manifolds of holonomy. We shall study this equation on the Bryant-Salamon manifolds. We construct examples of -monopoles on two of these manifolds, namely the total space of the bundle of anti-self-dual two forms over the $\ma…
Develops invariants for webs and foams using Seiberg-Witten theory.
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…