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.
The paper classifies extensions of Yang-Mills-type theories and their spaces.
Lin and Sjamaar have used symplectic Hodge theory to obtain canonical equivariant extensions for Hamiltonian actions on closed symplectic manifolds that have the strong Lefschetz property. Here we obtain canonical equivariant extensions much more generally by means of classical Hodge theory.
A new compact metrizable space Z replaces X in extension theory.
We explain how rank two Frobenius extensions of commutative rings lead to link homology theories and discuss relations between these theories, Bar-Natan theories, equivariant cohomology and the Rasmussen invariant.
The purpose of this contribution is to point out connections between recent ideas about gerbes and gerbal actions (as higher categorical extension of representation theory) and old discussion in quantum field theory on commutator anomalies, gauge group extensions, and 3-cocycles. The unifying concept is the classical o…
New cohomology theory for Lie 2-algebras extends classical theory.
Clarifies structures in link homology theories using Frobenius extensions.
The central extension of the Thompson group that arises in the quantized Teichmüller theory is 12 times the Euler class. This extension is obtained by taking a (partial) abelianization of the so-called braided Ptolemy-Thompson group introduced and studied in \cite{FK2}. We describe then the cyclic central extension…
The proof of Theorem 7.12 of "Uniqueness of smooth cohomology theories" by the authors of this note is not correct. The said theorem identifies the flat part of a differential extension of a generalized cohomology theory E with ER/Z (there called "smooth extension"). In this note, we give a correct proof. Moreover, we …
Paper describes linear extensions of multiple conjugation quandles using MCQ Alexander pairs.
Introduces fat Lie theory for Lie groupoids and algebroids.
Paper generalizes complex Brunn-Minkowski theory and proves new extension theorems.
We study non-abelian differentiable gerbes over stacks using the theory of Lie groupoids. More precisely, we develop the theory of connections on Lie groupoid -extensions, which we call "connections on gerbes", and study the induced connections on various associated bundles. We also prove analogues of the Bianchi id…
The paper extends fractional Laplacian theory using symmetric spaces and extension problems.
We study the representation theory of the quantum Teichmueller space when going to infinity in the classical Teichmueller space. The geometric ingredients are the extension of Thurston's shear coordinates to the augmented Teichmueller space and the study of the Weil-Petersson Poisson structure for this extension. The r…
The quandle homology theory is generalized to the case when the coefficient groups admit the structure of Alexander quandles, by including an action of the infinite cyclic group in the boundary operator. Theories of Alexander extensions of quandles in relation to low dimensional cocycles are developed in parallel to gr…
Paper describes how to extend multiple conjugation quandles using maps.
Unified treatment of gauge theories and Yang-Mills theory duality.
Proves conditions for black hole formation in Einstein-Maxwell theory.
Paper analyzes mathematical theory behind out-of-sample DR extensions.
Floer theory uses categories to construct 3-manifold invariants.
We present an approach to cohomological dimension theory based on infinite symmetric products and on the general theory of dimension called the extension dimension. The notion of the extension dimension $\ExD(X)$ was introduced by A.N.Dranishnikov \cite {D} in the context of compact spaces and CW complexes. This pa…
Study characterizes cohomology and homotopy types for M-theory extensions.
The paper classifies extensions of Yang-Mills-type theories, proving maximality and universality are dense properties.
Extends functions on symmetric spaces to analytic functions.
Obstruction theory for complex bigraded differential algebras.
Kan extensions help in data science extrapolation and learning.
Quandle cocycles are constructed from extensions of quandles. The theory is parallel to that of group cohomology and group extensions. An interpretation of quandle cocycle invariants as obstructions to extending knot colorings is given, and is extended to links component-wise.
Develops relative harmonic metrics and deformation theory for Higgs and flat bundles on compact Kähler manifolds.
Develops theory of Cartan geometries on skeletons and morphisms induced by extension functors.
Study extends holomorphic forms on noncompact Kahler manifolds.
The properties of the Riemann extensions of nonriemannian spaces defined by the first order systems of differential equations are considered.
The paper develops a Galois theory for cluster algebras and Riemann surfaces.
There is an equivalence relation on the set of smooth maps of a manifold into the stable unitary group, defined using a Chern-Simons type form, whose equivalence classes form an abelian group under ordinary block sum of matrices. This construction is functorial, and defines a differential extension of odd K-theory, fit…
New definitions of rack and quandle modules are introduced, and shown to generalise the definitions previously studied by Andruskiewitsch, Etingof and Grana. This new construct is shown to coincide with Beck's general definition of a module in an arbitrary category. A theory of Abelian extensions of racks and quandles …
This paper extends classical Galois theory to differential equations, linking it to geometry and mechanics.
Main mathematical applications of Frobenius manifolds are in the theory of Gromov - Witten invariants, in singularity theory, in differential geometry of the orbit spaces of reflection groups and of their extensions, in the hamiltonian theory of integrable hierarchies. The theory of Frobenius manifolds establishes rema…
Morse theory extended to non-degenerate functions.
We study holomorphic extensions of Matsuki orbits in complex Grassmannians.
Jets of mappings introduced by Ehresmann are still the most useful objects for formulating geometric frameworks of physical theories. We are proposing modifications designed to make jet theory less dependent on local coordinates. Extensions of the theory with applications to the calculus of variations and mechanics are…
We give a new interpretation of the Faddeev-Mickelsson anomaly in certain Yang-Mills theories in terms of S^1-central extensions of Lie groupoids.
Constructs new topological theories in 2D not fitting standard axioms.
The paper explores the connection between 3d gravity and Chern-Simons theory using affine group connections.
The main aim of this paper is the construction of a smooth (sometimes called differential) extension \hat{MU} of the cohomology theory complex cobordism MU, using cycles for \hat{MU}(M) which are essentially proper maps W\to M with a fixed U(n)-structure and U(n)-connection on the (stable) normal bundle of W\to M. Cruc…
It is well-known that classical two-dimensional topological field theories are in one-to-one correspondence with commutative Frobenius algebras. An important extension of classical two-dimensional topological field theories is provided by open-closed two-dimensional topological field theories. In this paper we extend o…
This paper extends group cohomology to bounded cohomology using quasihomomorphisms.
Smooth models refine topological K-theory for differential extensions.
Unified description of Weierstrass-type representations.