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 symplectic reduction and theorem to Lie algebroids.
Study of symplectic and Poisson reduction, proposing Poisson implosion.
Generalizes symplectic reduction to cosymplectic groupoid actions.
New proof for stable reduction theorem using Kähler-Einstein metrics.
We generalize reduction theorems for classical connections to operators with values in -th order natural bundles. Using the first reduction theorem in order two we classify all (0,2)-tensor fields on the cotangent bundle of a manifold with a linear (non-symmetric) connection.
Two reduction schemes for symplectic manifolds are shown equivalent.
The study proves a rigidity theorem for compact manifolds with boundary.
Introduces new algebraic structures for relational groupoids and proves a reduction theorem.
We introduce the notion of a Hamiltonian action of an étale Lie group stack on an étale symplectic stack and establish versions of the Kirwan convexity theorem, the Meyer-Marsden-Weinstein symplectic reduction theorem, and the Duistermaat-Heckman theorem in this context.
The version of Marsden-Ratiu reduction theorem for Nambu-Poisson manifolds by a regular distribution has been studied by Ibez et al. In this paper we show that the reduction is always ensured unless the distribution is zero. Next we extend the more general Falceto-Zambon Poisson reduct…
The paper explores polysymplectic structures and their reductions in field theories.
We consider dimension reduction for solutions of the Kähler-Ricci flow with nonegative bisectional curvature. When the complex dimension , we prove an optimal dimension reduction theorem for complete translating Kähler-Ricci solitons with nonnegative bisectional curvature. We also prove a general dimension reducti…
The purpose of this paper is to generalize the regular Optimal Reduction Theorem to general proper Dirac actions, formulated both in terms of point and orbit reduction. A comparison to general standard singular Dirac reduction is given emphasizing the desingularization role played by optimal reduction.
Proposes a new category of bundles for Lagrangian reduction in field theory.
Reduces Lie (bi-)algebroids and Dirac manifolds using constraint vector bundles.
Analyzes canonical reductive decomposition of extrinsic homogeneous submanifolds.
The paper proves rigidity theorems for forms on reductive symmetric spaces.
We extend the theorems concerning the equivariant symplectic reduction of the cotangent bundle to contact geometry. The role of the cotangent bundle is taken by the cosphere bundle. We use Albert's method for reduction at zero and Willett's method for non-zero reduction. We provide examples for both cases.
We complete the reduction scheme in the whole LP category, introduced in [7] to perform Lagrangian reduction by stages. We answer affirmatively the open question of whether reduction can be done in the whole category and analyze the Noether theorem on LP-bundles, the relationship with Hamiltonian reduction by stages an…
Reduces Poisson manifolds with Hamiltonian Lie algebroids.
A general study of symmetries in optimal control theory is given, starting from the presymplectic description of this kind of system. Then, Noether's theorem, as well as the corresponding reduction procedure (based on the application of the Marsden-Weinstein theorem adapted to the presymplectic case) are stated both in…
In a previous article, we introduced a reduction procedure for locally conformally symplectic manifolds at any regular value of the momentum mapping. We use this construction to prove an analogue of a well-known theorem in the symplectic setting about the reduction of cotangent bundles.
The X-ADM mass is shown to be equivalent to the ADM mass, proving the X-positive mass theorem in all dimensions.
In this paper we show as main results two structure theorems of a compact homogeneous locally conformally Kaehler (or shortly l.c.K.) manifold, a holomorphic structure theorem asserting that it has a structure of holomorphic principal fiber bundle over a flag manifold with fiber a 1-dimensional complex torus, and a met…
The purpose of these survey notes is to give a presentation of a classical theorem of Nomizu that relates the invariant affine connections on reductive homogeneous spaces and nonassociative algebras.
Theory of symplectic reduction in infinite dimensions developed.
Develops a reduction theory for covariant field theories with gauge symmetries.
In this article, we give a theorem of reduction of the structure group of a principal bundle P with regular structure group G. Then, when G is in the classes of Lie groups defined by T.Robart [13], we define the closed holonomy group of a connection as the minimal closed Lie subgroup of G for which the previous theorem…
The paper extends a theorem to number fields without infinite places.
After defining generalizations of the notions of covariant derivatives and geodesics from Riemannian geometry for reductive Cartan geometries in general, various results for reductive Cartan geometries analogous to important elementary results from Riemannian geometry are proven using these generalizations. In particul…
Bregman divergences play a central role in the design and analysis of a range of machine learning algorithms. This paper explores the use of Bregman divergences to establish reductions between such algorithms and their analyses. We present a new scaled isodistortion theorem involving Bregman divergences (scaled Bregman…
The paper simplifies symmetries in complex geometric structures.
We prove a reduction theorem for the tangent bundle of a Poisson manifold endowed with a pre-Hamiltonian action of a Poisson Lie group . In the special case of a Hamiltonian action of a Lie group, we are able to compare our reduction to the classical Marsden-Ratiu reduction of . If the manifold $M…
Reduction principles for proper actions on smooth manifolds.
The paper introduces controllable principal connections and estimates distances between bundles and spaces.
We previously extended the Marsden-Ratiu reduction theorem in Poisson geometry by means of graded geometry (see Part I of Arxiv:1009.0948) . In this note we provide the background material about graded geometry necessary for the proof. Further, we provide an alternative algebraic proof.
Introduces generalized moment maps for almost Hermitian settings.
We prove a version of the affine Kempf-Ness theorem for non-algebraic symplectic structures and shifted moment maps, and use it to describe hyperkahler quotients of T*G, where G is a complex reductive group.
Contact Lie systems analyze integral curves of Hamiltonian vector fields.
We present a reduction of codimension theorem for surfaces with parallel mean curvature in symmetric spaces.
Established a generalized Boothby-Wang theorem in contact geometry.
In this paper an extended CPR decomposition theorem for Finsler symmetric spaces of semi-negative curvature in the context of reductive structures is proven. This decomposition theorem is applied to give a geometric description of the complexification of some infinite dimensional homogeneous spaces.
We prove a Simons-type holonomy theorem for totally skew 1-forms with values in a Lie algebra of linear isometries. The only transitive case, for this theorem, is the full orthogonal group. We only use geometric methods and we do not use any classification (not even that of transitive isometric actions on the sphere or…
Theorem proves congruence for compact submanifolds in a sphere.
In this paper, we first study the Poisson reductions of controlled Hamiltonian (CH) system and symmetric CH system by controllability distributions. These reductions are the extension of Poisson reductions by distribution for Poisson manifolds to that for phase spaces of CH systems with external force and control. We g…
We prove several versions of "quantization commutes with reduction" for circle actions on manifolds that are not symplectic. Instead, these manifolds possess a weaker structure, such as a spin^c structure. Our theorems work whenever the quantization data and the reduction data are compatible; this condition always hold…
We use the Dold-Whitney theorem classifying -bundles over a 4-complex to give a mod 4 obstruction to a 2-component link of trivial linking number being slice. It turns out that this coincides with the reduction of the Sato-Levine invariant.
We present a modern formulation of Élie Cartan's structure theory for Lie pseudogroups and prove a reduction theorem that clarifies the role of Cartan's systatic system. The paper is divided into three parts. In part one, using notions coming from the theory of Lie groupoids and algebroids, we introduce the framework o…