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.
Defines holonomy for Lie algebroid representations up to homotopy.
In the first part of this paper, we work out a perturbative Lagrangian formulation of semistrict higher gauge theory, that avoids the subtleties of the relationship between Lie 2-groups and algebras by relying exclusively on the structure semistrict Lie 2-algebra v and its automorphism 2-group Aut(v). Gauge transformat…
Defines symplectic 2-groupoids and their relation to Courant algebroids.
Homflypt skein theory and string topology linked via 2-groupoids.
The abstract discusses Lie 2-groupoids and their applications in representation theory.
Formally equates two quantization methods and constructs non-commutative algebras.
We apply the bar construction to the nerve of a double Lie groupoid to obtain a local Lie 2-groupoid. As an application, we recover Haefliger's fundamental groupoid from the fundamental double groupoid of a Lie groupoid. In the case of a symplectic double groupoid, we study the induced closed 2-form on the associated l…
Defines duals of higher vector bundles for Lie 2-groupoids.
We construct an infinite-dimensional symplectic 2-groupoid as the integration of an exact Courant algebroid. We show that every integrable Dirac structure integrates to a "Lagrangian" sub-2-groupoid of this symplectic 2-groupoid. As a corollary, we recover a result of Bursztyn-Crainic-Weinstein-Zhu that every integrabl…
Following Sullivan's spacial realization of a differential algebra, we construct a universal integrating Lie 2-groupoid for every Lie algebroid. Then We show that unlike Lie algebras which one-to-one correspond to simply connected Lie groups, Lie algebroids (integrable or not) one-to-one correspond to a sort of etale L…
We identify the 2-groupoid of deformations of a gerbe on a smooth manifold with the Deligne 2-groupoid of a corresponding twist of the DGLA of local Hochschild cochains on infinite jets of smooth functions.
The paper classifies equivariant gerbe connections on Lie groups.
Paper defines PB-groupoids and their relation to VB-groupoids.
In this paper, we describe an integration of exact Courant algebroids to symplectic 2-groupoids, and we show that the differentiation procedure from [26] inverts our integration.
We establish a functor from local Kan simplicial manifolds to weak Kan simplicial manifolds. It gives a solution to the problem of extending local Lie groupoids to Lie 2-groupoids.
We show that for a differential graded Lie algebra whose components vanish in degrees below -1 the nerve of the Deligne 2-groupoid is homotopy equivalent to the simplicial set of -valued differential forms introduced by V.Hinich.
Abstract: New geometric incarnation of isomonodromy functors.
We study the extension of a Lie algebroid by a representation up to homotopy, including semidirect products of a Lie algebroid with such representations. The extension results in a higher Lie algebroid. We give exact Courant algebroids and string Lie 2-algebras as examples of such extensions. We then apply this to obta…
Usually bundle gerbes are considered as objects of a 2-groupoid, whose 1-morphisms, called stable isomorphisms, are all invertible. I introduce new 1-morphisms which include stable isomorphisms, trivializations and bundle gerbe modules. They fit into the structure of a 2-category of bundle gerbes, and lead to natural d…
We discuss two sorts of generalization of Lie groupoids. One is Lie -groupoids defined as simplicial manifolds with trivial . The other is the stacky Lie groupoid $\cG\rra M$ with $\cG$ a differentiable stack. We build 1-1 correspondence between Lie 2-groupoids and stacky Lie groupoids up to a certain…
We prove that the groupoid of transformations of rigid structures on surfaces has a finite presentation as a 2-groupoid establishing a result first conjectured by G.Moore and N.Seiberg. An alternative proof was given by B.Bakalov and A.Kirillov Jr. We present some applications to TQFTs. This is also related to recent w…
We discuss two generalizations of Lie groupoids. One consists of Lie -groupoids defined as simplicial manifolds with trivial . The other consists of stacky Lie groupoids $\cG\rra M$ with $\cG$ a differentiable stack. We build a 1-1 correspondence between Lie 2-groupoids and stacky Lie groupoids up to …
We establish a relation between smooth 2-functors defined on the path 2-groupoid of a smooth manifold and differential forms on this manifold. This relation can be understood as a part of a dictionary between fundamental notions from category theory and differential geometry. We show that smooth 2-functors appear in se…
We prove a Darboux theorem for formal deformations of Hamiltonian operators of hydrodynamic type (Dubrovin-Novikov). Not all deformations are equivalent to the original operator: there is a moduli 2-stack of normal forms. The paper utilizes three main concepts: 1) dg Lie algebras concentrated in degrees [-1,\infty) suc…
In this thesis, we employ simplicial methods to study actions, principal bundles, and bibundles of higher groupoids. Roughly, we use Kan fibrations to model actions of higher groupoids, we use pairs of a Kan fibration and a special acyclic fibration to model principal bundles of higher groupoids, we use inner Kan fibra…
We find canonical gauges for higher gauge theories in 2- and 3-gauge theories.
Paper introduces Tensor Gauge Flow Models for better data encoding.
L-CNNs preserve gauge symmetry in lattice simulations.
Develops a new approach to describe gauge theories with background fields using presymplectic structures.
L-CNNs learn gauge invariant quantities on lattices.
L-CNNs preserve gauge symmetry in neural networks.
New discretization method for gauge theories preserves gauge invariance rigorously.
When a gauge-natural invariant variational principle is assigned, to determine {\em canonical} covariant conservation laws, the vertical part of gauge-natural lifts of infinitesimal principal automorphisms -- defining infinitesimal variations of sections of gauge-natural bundles -- must satisfy generalized Jacobi equat…
Defines gauge transformations for Jacobi structures and their effects on contact groupoids.
We propose a general notion of algebraic gauge theory obtained via extracting the main properties of classical gauge theory. Building on a recent work on transferring curved -structures we show that, under certain technical conditions, algebraic gauge theories can be transferred along chain contractions. Sp…
We consider dimensional reduction of gauge theories with arbitrary gauge group in a formalism based on equivariant principal bundles. For the classical gauge groups we clarify the relations between equivariant principal bundles and quiver bundles, and show that the reduced quiver gauge theories are all generically buil…
Researchers derive symmetry operators from twistor spinors in curved spacetime.
L-CNNs maintain gauge symmetry on non-Abelian lattice theories.
Gauge Flow Models use a learnable Gauge Field in Generative Flow Models.
Extends gauge conditions for superparticle to conic neighbourhood.
Lecture notes on gauge theory for manifold invariants.
The Kuperberg invariant is shown to be gauge invariant for certain framed 3-manifolds.
Study gauge groups over high-dimensional manifolds, showing homotopy decompositions.
The paper gauges non-linear sigma models using Lie algebroid actions.
We study gauge transformations of Dirac structures and the relationship between gauge and Morita equivalences of Poisson manifolds. We describe how the symplectic structure of a symplectic groupoid is affected by a gauge transformation of the Poisson structure on its identity section, and prove that gauge-equivalent in…
We consider the problem of existence of representations of topological groupoids on a principal bundle and the classification of such representations up to gauge transformation. Such representations naturally occur in various contexts such as gauge theory, lattice gauge fields, equivariant bundles, etc. In the course o…
Develops a new sampling method for gauge theories.
Area law proven for 2D Yang-Mills in generalized axials.