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 universal link invariants from intersections in configuration spaces.
The universal sl_2 invariant of string links has a universality property for the colored Jones polynomial of links, and takes values in the h-adic completed tensor powers of the quantized enveloping algebra of sl_2. In this paper, we exhibit explicit relationships between the universal sl_2 invariant and Milnor invaria…
GCNNs gain rotation invariance with more training augmentation, making SVD-Universal more effective.
New invariant fully describes finite type invariants of knots in homology 3-spheres.
New derivation of knot invariants from universal invariant.
A universal collection of 4 invariants improves neural network accuracy for molecular dynamics.
Refines a tangle invariant using XC-algebras.
We extend the theory of the universal eta-invariant to the case of relative bordism groups of manifolds with boundaries. This allows the construction of secondary descendants of the universal eta-invariant. We obtain an interpretation of Laures' f-invariant as an example of this general construction. As an aside we imp…
Study of Gödel Universe as Lie group with specific metric.
In this paper, we define finite type invariants for cyclic equivalence classes of nanophrases and construct the universal ones. Also, we identify the universal finite type invariant of degree 1 essentially with the linking matrix. It is known that extended Arnold's basic invariants to signed words are finite type invar…
New basis for quantum gl_N invariants derived from Macdonald polynomials.
The Drinfeld double of a finite dimensional Hopf algebra is a quasi-triangular Hopf algebra with the canonical element as the universal -matrix, and one can obtain a ribbon Hopf algebra by adding the ribbon element. The universal quantum invariant of framed links is constructed using a ribbon Hopf algebra. In that c…
New geometric invariant from disc intersections captures all coloured Jones polynomials.
In this paper, we study relations among known universal equations for Gromov-Witten invariants at genus 1 and 2.
The universal sl_2 invariant of bottom tangles has a universality property for the colored Jones polynomial of links. Habiro conjectured that the universal sl_2 invariant of boundary bottom tangles takes values in certain subalgebras of the completed tensor powers of the quantized enveloping algebra U_h(sl_2) of the Li…
The Euler characteristic is the only additive topological invariant for spaces of certain sort, in particular, for manifolds with some finiteness properties. A generalization of the notion of a manifold is the notion of a V-manifold. Here we discuss a universal additive topological invariant of V-manifolds: the univers…
Group invariant and equivariant Multilayer Perceptrons (MLP), also known as Equivariant Networks, have achieved remarkable success in learning on a variety of data structures, such as sequences, images, sets, and graphs. Using tools from group theory, this paper proves the universality of a broad class of equivariant M…
Study extends Vogel's universality to torus knots in adjoint representation.
In this article we present infinitely many 3-manifolds admitting infinitely many universally tight contact structures each with trivial Ozsvath-Szabo contact invariants. By known properties of these invariants the contact structures constructed here are non weakly symplectically fillable.
We present a universal knot polynomials for 2- and 3-strand torus knots in adjoint representation, by universalization of appropriate Rosso-Jones formula. According to universality, these polynomials coincide with adjoined colored HOMFLY and Kauffman polynomials at SL and SO/Sp lines on Vogel's plane, and give their ex…
Constraining linear layers in neural networks to respect symmetry transformations from a group is a common design principle for invariant networks that has found many applications in machine learning. In this paper, we consider a fundamental question that has received little attention to date: Can these networks ap…
New quantum knot invariants derived from Verma modules.
We show that the perturbative invariant of rational homology 3-spheres can be recovered from the LMO invariant for any simple Lie algebra , i.e, the LMO invariant is universal among the perturbative invariants. This universality was conjectured in [25]. Since the perturbative invariants dominate …
Study models of Gödel Universe using Lie groups and Iwasawa decomposition.
A `total Chern class' invariant of knots is defined. This is a universal Vassiliev invariant which is integral `on the level of Lie algebras' but it is not expressible as an integer sum of diagrams. The construction is motivated by similarities between the Kontsevich integral and the topological Chern character.
We define combinatorial invariants of Legendrian and transverse links in universally tight lens spaces using grid diagrams, generalizing [OST08] and prove that they are equivalent to the invariants defined in [BVVV13] and [LOSS09]. We use these combinatorial invariants to characterize index one grid diagrams for knots …
In the setting of finite type invariants for null-homologous knots in rational homology 3-spheres with respect to null Lagrangian-preserving surgeries, there are two candidates to be universal invariants, defined respectively by Kricker and Lescop. In a previous paper, the second author defined maps between spaces of J…
We define a graph algebra version of the stationary phase integration over the coadjoint orbits in the Reshetikhin formula for the colored Jones-HOMFLY polynomial. As a result, we obtain a `universal' U(1)-RCC invariant of links in rational homology spheres, which determines the U(1)-RCC invariants based on simple Lie …
In this paper we describe the Seiberg-Witten invariants, which have been introduced by Witten, for manifolds with . In this case the invariants depend on a chamber structure, and there exists a universal wall crossing formula. For every Kähler surface with and =0, these invariants are non-trivial for …
We present a simple proof for the universality of invariant and equivariant tensorized graph neural networks. Our approach considers a restricted intermediate hypothetical model named Graph Homomorphism Model to reach the universality conclusions including an open case for higher-order output. We find that our proposed…
The study constructs universal invariants for non-Archimedean metrics on projective varieties.
Kernel methods have been widely applied to machine learning and other questions of approximating an unknown function from its finite sample data. To ensure arbitrary accuracy of such approximation, various denseness conditions are imposed on the selected kernel. This note contributes to the study of universal, characte…
In this paper, we develop a theory about the relationship between -invariant/equivariant functions and deep neural networks for finite group . Especially, for a given -invariant/equivariant function, we construct its universal approximator by deep neural network whose layers equip -actions and each affine t…
New invariant counts graph configurations in 3D manifolds.
Researchers prove no unexpected relations between complex manifold numbers.
Counterexample found for Stein property of certain solvable Lie groups.
We study the conformally invariant variational problem for time-like curves in the -dimensional Einstein universe defined by the conformal strain functional. We prove that the stationary curves are trapped into an Einsetin universe of dimension , or . We study the linearly-full stationary curves in a four-…
In the present paper, we study the finite type invariants of Gauss words. In the Polyak algebra techniques, we reduce the determination of the group structure to transformation of a matrix into its Smith normal form and we give the simplified form of a universal finite type invariant by means of the isomorphism of this…
New approach to quantum knot invariants using perturbed Gaussian generating functions.
We give a new and simple proof for the computation of the oriented and the unoriented fold cobordism groups of Morse functions on surfaces. We also compute similar cobordism groups of Morse functions based on simple stable maps of 3-manifolds into the plane. Furthermore, we show that certain cohomology classes associat…
Paper introduces 'zippers' for constructing universal circles.
Study presents a method to induce a generalized neural network from joint group invariant functions.
New weight systems derived from a specific Lie algebra for knot invariants.
The integrality of the Kontsevich integral and perturbative invariants is discussed. We show that the denominator of the degree part of the Kontsevich integral of any knot or link is a divisor of . We also show that the denominator of of the degree part of the universal perturbative invari…
This work establishes universality for deep equivariant networks, overcoming limitations of previous approaches.
New universal invariant operators are introduced in a class of geometries which include the quaternionic structures and their generalisations as well as 4-dimensional conformal (spin) geometries. It is shown that, in a broad sense, all invariants and invariant operators arise from these universal operators and that the…
Study of universal complexes in toric topology with applications in category theory.
We establish blow-up profiles for any blowing-up sequence of solutions of general conformally invariant fully nonlinear elliptic equations on Euclidean domains. We prove that (i) the distance between blow-up points is bounded from below by a universal positive number, (ii) the solutions are very close to a single stand…