Related papers: Hyperbolic monopoles with continuous symmetries
We use Dehn surgery methods to construct infinite families of hyperbolic knots in the 3-sphere satisfying a weak form of the Turaev--Viro invariants volume conjecture. The results have applications to a conjecture of Andersen, Masbaum, and…
We study the compactness problem for moduli spaces of holomorphic supercurves which, being motivated by supergeometry, are perturbed such as to allow for transversality. We give an explicit construction of limiting objects for sequences of…
We introduce the Hyperbolic Higgs, a novel solution to the little hierarchy problem that features Standard Model neutral scalar top partners. At one-loop order, the protection from ultraviolet sensitivity is due to an accidental non-compact…
Magnetic monopoles in hyperbolic space are in correspondence with certain algebraic curves in mini-twistor space, known as spectral curves, which are in turn in correspondence with rational maps between Riemann spheres. Hyperbolic monopoles…
We present a classification of all spherical indecomposable representations of classical and exceptional Lie superalgebras. We also include information about stabilizers, symmetric algebras, and Borels for which sphericity is achieved. In…
We show that a partially hyperbolic system can have at most a finite number of compact center-stable submanifolds. We also give sufficient conditions for these submanifolds to exist and consider the question of whether they can intersect…
We classify the boundaries of hyperbolic groups that have enough quasiconvex codimension-1 surface subgroups with trivial or cyclic intersections.
Motivated by the initial-boundary value problem for the Einstein equations, we propose a definition of symmetric hyperbolicity for systems of evolution equations that are first order in time but second order in space. This can be used to…
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.
We consider closed hypersurfaces smoothly immersed in hyperbolic manifolds up to homotopy and commensurability. We prove that if a closed hyperbolic manifold $M$ contains a sequence of asymptotically geodesic hypersurfaces, then $\pi_1(M)$…
The moduli spaces of hyperbolic monopoles are naturally fibred by the monopole mass, and this leads to a nontrivial mass dependence of the holomorphic data (spectral curves, rational maps, holomorphic spheres) associated to hyperbolic…
We present the general properties of dynamic dissipative fluid distribution endowed with hyperbolical symmetry. All the equations required for its analysis are exhibited and used to contrast the behavior of the system with the spherically…
An important problem in quaternionic hyperbolic geometry is to classify ordered $m$-tuples of pairwise distinct points in the closure of quaternionic hyperbolic n-space, $\overline{{\bf H}_\bh^n}$, up to congruence in the holomorphic…
Assuming that every hyperbolic group is residually finite, we prove the congruence subgroup property for mapping class groups of hyperbolic surfaces of finite type. Under the same assumption, it follows that profinitely equivalent…
A new method for the Lie group classification of differential equations is proposed. It is based of the determination of all possible cases of linear dependence of certain indeterminate appearing in the determining equations of symmetries…
Consider a relatively hyperbolic group G. We prove that if G is finitely presented, so are its parabolic subgroups. Moreover, a presentation of the parabolic subgroups can be found algorithmically from a presentation of G, a solution of its…
In this paper, we review the progress in the analysis of magnetic monopoles as generalized states in quantum mechanics. We show that the considered model contains rich algebraic structure that generates symmetries which have been utilized…
Embedding the data in hyperbolic spaces can preserve complex relationships in very few dimensions, thus enabling compact models and improving efficiency of machine learning (ML) algorithms. The underlying idea is that hyperbolic…
An interesting question about quasiconvexity in a hyperbolic group concerns finding classes of quasiconvex subsets that are closed under finite intersections. A known example is the class of all quasiconvex subgroups. However, not much is…
We prove several topological and dynamical properties of the boundary of a hierarchically hyperbolic group are independent of the specific hierarchically hyperbolic structure. This is accomplished by proving that the boundary is invariant…