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.
Extends dualities in supergravity to broader setups.
In this note we consider the relationship between the dressing action and the holonomy representation in the context of constant mean curvature surfaces. We characterize dressing elements that preserve the topology of a surface and discuss dressing by simple factors as a means of adding bubbles to a class of non finite…
The aim of this paper is to give a new link between integrable systems and minimal surface theory. The dressing operation uses the associated family of flat connections of a harmonic map to construct new harmonic maps. Since a minimal surface in 3-space is a Willmore surface, its conformal Gauss map is harmonic and a d…
We construct unitary modular categories for a general class of coset conformal field theories based on our previous study of these theories in the algebraic quantum field theory framework using subfactor theory. We also consider the calculations of the corresponding 3-manifold invariants. It is shown that under certain…
All polynomial invariants of links for two dimensional solutions of Yang-Baxter equation is constructed by employing Turaev's method. As a consequence, it is proved that the best invariant so constructed is the Jones polynomial and there exist three solutions connecting to the Alexander polynomial. Invariants for highe…
The paper extends group constructions to coset geometries, creating new ways to combine geometries.
We present a loop group description for curves in , and apply it to classify the circletons: Circles dressed by simple factors.
We investigate the dressing action on surfaces of constant mean curvature (CMC surfaces) in Euclidean space. In particluar, we show that for CMC surfaces with umbilics the isotropy group under dressing is always trivial. This result is applied to the investigation of CMC surfaces whose metric is invariant under a group…
Develops intrinsic curved cosets for Cartan geometries.
We characterize Bianchi-Bäcklund transformations of surfaces of positive constant Gauss curvature in terms of dressing actions of the simplest type on the space of harmonic maps.
Solves double coset problem for braid group H_n.
We use the dressing method to construct transformations of constrained Willmore surfaces in arbitrary codimension. An adaptation of the Terng--Uhlenbeck theory of dressing by simple factors to this context leads us to define Bäcklund transforms of these surfaces for which we prove Bianchi permutability. Specialising to…
The study of double coset growth in specific groups confirms a conjecture about generic 3-manifolds.
We define and study the Burnside quotient Green ring of a Mackey functor. Some refinements of Dress induction theory are presented, together with applications to computation results for -theory and -theory of finite and infinite groups.
Mapping class group subgroups yield quasi-isometric curve complex.
Geometric methods show cosets of mapping class groups for 3-manifolds.
COSET benchmarks neural program embeddings using diverse source-code datasets.
We translate a classification scheme for periodic CMC surfaces developed by J. Dorfmeister and the author to discrete CMC surfaces in the sense of A. Bobenko and U. Pinkall. The scheme uses the dressing action on discrete CMC surfaces to arrive at a classification for periodic discrete CMC surfaces.
The paper studies conformal and projective structures using 2-frame bundles.
We prove that the Cayley graph and the coset geometry of the von Dyck group are linked by a vertex-to-edge duality.
We classify the simplest rational elements in a twisted loop group, and prove that dressing actions of them on proper indefinite affine spheres give the classical Tzitzéica transformation and its dual. We also give the group point of view of the Permutability Theorem, construct complex Tzitzéica transformations, and di…
We will first clarify the loop group formulations for both hyperbolic and elliptic definite affine spheres in R^3. Then we classify the rational elements with 3 poles or 6 poles in a real twisted loop group, and compute dressing actions of them on such surfaces. Some new examples with pictures will be produced at last.
Paper explores link and plat presentations, showing equivalence under bridge isotopy.
In this paper, we formulate a construction of ideal coset invariants for surface-links in -space using invariants for knots and links in -space. We apply the construction to the Kauffman bracket polynomial invariant and obtain an invariant for surface-links called the Kauffman bracket ideal coset invariant of sur…
Proves cosets of certain subgroups in hyperbolic 3-manifold groups are conjugacy distinguished.
We define a transformation on harmonic maps from a Riemann surface into the 2-sphere which depends on a complex parameter, the so-called mu-Darboux transformation. In the case when the harmonic map N is the Gauss map of a constant mean curvature surface f and the parameter is real, the mu-Darboux transformation of -N i…
Mathematical tools for tiling hyperbolic surfaces are developed.
Unified representation for minimal and constant mean curvature surfaces.
The Cayley graph of quandles reveals structural properties and is studied for various classes.
Researchers develop Orlov-Schulman symmetries for self-dual conformal structures.
We propose a Poisson-Lie analog of the symplectic induction procedure, using an appropriate Poisson generalization of the reduction of symplectic manifolds with symmetry. Having as basic tools the equivariant momentum maps of Poisson actions, the double group of a Poisson-Lie group and the reduction of Poisson manifold…
Study shows stable graphs in Heisenberg group are essentially planes.
Paper classifies fibers of fat Riemannian submersions with non-negative curvature.
We discuss constant mean curvature bubbletons in Euclidean 3-space via dressing with simple factors, and prove that single bubbletons are not embedded.
Robot-assisted dressing offers an opportunity to benefit the lives of many people with disabilities, such as some older adults. However, robots currently lack common sense about the physical implications of their actions on people. The physical implications of dressing are complicated by non-rigid garments, which can r…
Gauge symmetries are a cornerstone of modern physics but they come with technical difficulties when it comes to quantization, to accurately describe particles phenomenology or to extract observables in general. These shortcomings must be met by essentially finding a way to effectively reduce gauge symmetries. We propos…
Unified view of integrable systems linking CMC, isothermic, and Willmore surfaces.
In this paper, we use the technique of Finslerian submersion to deduce a flag curvature formula for homogeneous Finsler spaces. Based on this formula, we give a complete classification of even-dimensional smooth coset spaces admitting -invariant Finsler metrics with positive flag curvature. It turns out that t…
The quantum cohomology of CP^1 is generated by some potential (Frobenius manifold) that also has an interpretation as a potential of some harmonic map. Actually, the potential induces harmonic maps into three different symmetric spaces and each of these harmonic maps induces an immersion of an integrable surface. The f…
New methods convert complex link presentations to simpler, recognizable forms.
We study the harmonic map equations for maps of a Riemann surface into a Riemannian symmetric space of compact type from the point of view of soliton theory. There is a well-known dressing action of a loop group on the space of harmonic maps and we discuss the orbits of this action through particularly simple harmonic …
Strong bolicity helps prove Baum-Connes conjecture for certain hyperbolic groups.
Complex captures group properties, invariant under quasi-isometry.
The paper explores reductions of self-dual conformal structure equations.
Let M = H^3 / Γbe a hyperbolic 3-manifold of finite volume. We show that if H and K are abelian subgroups of Γand g is in Γ, then the double coset HgK is separable in Γ. As a consequence we prove that if M is a closed, orientable, Haken 3-manifold and the fundamental group of every hyperbolic piece of the torus decompo…
A geometric account explains why 'The Dress' is ambiguous, predicting observable signatures in image processing.
We give a survey of the following six closely related topics: (i) a general method for constructing a soliton hierarchy from a splitting of a loop algebra into positive and negative subalgebras, together with a sequence of commuting positive elements, (ii) a method---based on (i)---for constructing soliton hierarchies …
In this paper, we introduce the flag-wise positively curved condition for Finsler spaces (the (FP) Condition), which means that in each tangent plane, we can find a flag pole in this plane such that the corresponding flag has positive flag curvature. Applying the Killing navigation technique, we find a list of compact …