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.
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48 results for “bundle methods”
The paper studies conformal and projective structures using 2-frame bundles.
problem Understanding connections between conformal and projective structures.
method Using the dressing field method to obtain local, gauge invariant connections.
result A projective tractor bundle can be defined using the same construction as for conformal structures.
Study on stable vector bundles over Gauduchon manifolds.
problem Existence and stability of vector bundles over Gauduchon manifolds.
method Uhlenbeck--Yau's continuity method for approximate Hermitian--Einstein structures.
result Equivalence of semi-stability and existence of Hermitian--Einstein structures.
A new method solves convex optimization on curved spaces.
problem Optimization on curved spaces with non-smooth functions.
method Convex bundle method on Riemannian manifolds.
result The method converges to a minimizer under mild conditions.
Study character varieties of hyperbolic 3-manifolds using bundle methods.
problem Character varieties of hyperbolic 3-manifolds in once-punctured torus bundles.
method Restrict characters to the fibre and analyze branched covering maps.
result Infinite family of hyperbolic once-punctured bundles with unbounded genus.
Direct method finds Yang-Mills connections for SO(3) bundles.
problem Finding Yang-Mills connections for SO(3) bundles over closed 4-manifolds.
method Direct minimizing method with test connections and assumptions.
result Minimizing sequence converges to a minimizer or anti-selfdual/selfdual connection.
Study on Gauduchon manifolds finds metrics for projectively flat bundles.
problem Existence of Hermitian-Poisson metrics on projectively flat bundles.
method Heat flow techniques and continuity methods.
result Established a correspondence between Hermitian-Poisson metrics and semi-simplicity.
Directly applies Kazdan--Warner results to prescribe scalar curvature on bundles.
problem Prescribing scalar curvature functions on bundles.
method Direct application of Kazdan--Warner results and variational methods.
result Determines which functions are realizable as scalar curvature functions on bundles.
Explicit String bundlesmath.DG
Method constructs 2-bundles over homogeneous spaces.
problem Lack of explicit examples of 2-bundles with specific structure groups.
method Constructs 2-bundles over homogeneous spaces using a method outlined.
result Explicit formulas for Cech cocycles are provided.
Construct Hermitian-Einstein metrics on stable holomorphic vector bundles using dynamical methods.
problem Constructing Hermitian-Einstein metrics on stable holomorphic vector bundles
method Dynamical construction
result Provided a dynamical construction of Hermitian-Einstein metrics on stable holomorphic vector bundles
Extensions of Higgs Bundlesmath.AG
We prove a Hitchin-Kobayashi correspondence for extensions of Higgs bundles. The results generalize known results for extensions of holomorphic bundles. Using Simpson's methods, we construct moduli spaces of stable objects. In an appendix we construct Bott-Chern forms for Higgs bundles
Classifies and constructs intertwining differential operators between line and vector bundles over real projective space.
problem Classifying and constructing intertwining differential operators between line and vector bundles over real projective space.
method F-method for classification and construction of intertwining differential operators.
result Generalizes a classical result of Bol for and classifies intertwining operators for .
Constructs moduli stacks of quiver bundles and applies to Higgs bundles.
problem Classifying morphisms of vector bundles over a fixed base.
method General method for constructing moduli stacks of diagrams of vector bundles indexed by a simplicial set.
result Recovery of Nakajima quiver varieties and alternate construction of moduli stacks of Higgs bundles.
New method for foliated bundles using holonomy groupoids.
problem Constructing holonomy groupoids for foliated bundles.
method Partial connection on diffeological principal bundle of germs.
result New hierarchy of holonomy groupoids for foliated bundles.
Proves Arnol'd's chord conjecture for conormal bundles.
problem Proving Arnol'd's chord conjecture for Legendrian submanifolds.
method Isomorphism between wrapped Floer cohomology and path space homology with coefficients in a local system, plus a twisted Hurewicz theorem.
result Proves chord conjecture for conormal bundles.
We give a method to construct stable vector bundles whose rank divides the degree over curves of genus bigger than one. The method complements the one given by Newstead. Finally, we make some systematic remarks and observations in connection with rationality of moduli spaces of stable vector bundles.
Solved Demailly systems for Vortex bundles on manifolds.
problem Equivalence of Hartshorne ampleness and Griffiths positivity for vector bundles.
method Applied the continuity method to prove smooth solutions for the Vortex bundle.
result Smooth solutions exist for the proposed Demailly systems.
New method constructs degenerate Sasakian manifolds from hyperkähler bundles.
problem Constructing degenerate --Sasakian manifolds.
method Using fiber products of Boothby-Wang bundles over hyperkähler manifolds.
result No non-trivial compact examples exist, and one family of nilpotent Lie groups with this geometry is identified.
Functional-analytic method for stochastic parallel transport in bundles.
problem Stochastic parallel transport in Hermitian bundles over Riemannian manifolds.
method Purely functional-analytic construction.
result Obtained a general Feynman-Kac formula in vector bundles.
In this paper we present a construction of stable bundles on Calabi-Yau threefolds using the method of bundle extensions. This construction applies to any given Calabi-Yau threefold with h^{1,1}>1. We give examples of stable bundles of rank 2 and 4 constructed out of pure geometric data of the given Calabi-Yau space. A…
Develops method to create non-Abelian Ricci-flat graphs via bundles.
problem Creating non-Abelian Ricci-flat graphs.
method Develops systematic way via graph bundles with constraints.
result Non-trivial graph bundles are not isomorphic to product of base and fiber.
The existence problem for holomorphic structures on vector bundles over non-algebraic surfaces is in general still open. We solve this problem in the case of rank 2 vector bundles over K3 surfaces and in the case of vector bundles of arbitrary rank over all known surfaces of class VII. Our methods, which are based on D…
Normal tractor conformal bundles and codimension two spacelike submanifolds in Lorentzian manifoldsmath.DG
A method constructs tractor conformal bundles for spacelike submanifolds in Lorentzian manifolds.
problem Characterize conditions for a tractor conformal bundle to be standard and normal.
method Introduce a canonical construction of a tractor conformal bundle and characterize conditions for it to be standard and normal.
result Characterizes conditions for a tractor conformal bundle to be standard and normal.
Paper proposes a method to estimate consumer valuations from bundle sales data.
problem Estimating consumer valuations from bundle sales data using classical methods is challenging.
method Proposes an approach using EM algorithm and Monte Carlo simulation to estimate consumer valuations from bundle sales data.
result The approach can recover the distribution of consumers' valuations and is robust to unobserved no-purchases and clustered market segments.
Using -methods for the -equation we prove that the Ohsawa-Takegoshi extension theorem also holds for holomorphic sections of a vector bundle, over compact Kähler manifolds. We then proceed to show that the conditions that are needed are more liberal than the ones one would need if one instead reduced…
The paper proves a theorem about constructing Higgs bundle moduli space.
problem Constructing the moduli space of Higgs bundles on a closed Riemann surface.
method Uses Kuranishi slice method and GIT quotient to prove the moduli space is a complex space locally modeled on a quadratic cone.
result The moduli space of Higgs bundles is a complex space locally modeled on an affine GIT quotient of a quadratic cone.
Newton's method tackles nonlinear mappings into vector bundles with connections and retractions.
problem Finding zeros of mappings from a manifold into a vector bundle.
method Local convergence using differentiability concepts, Banach space Riemannian distance, and affine covariant damping strategy.
result Illustrated application to generalized non-symmetric eigenvalue problems.
We discuss nonabelian bundle gerbes and their differential geometry using simplicial methods. Associated to any crossed module there is a simplicial group NC, the nerve of the 1-category defined by the crossed module and its geometric realization |NC|. Equivalence classes of principal bundles with structure group |NC| …
Two new classes of metrizable vector bundles have been presented in the papers [1] and [4]. The Lie algebroid generalized tangent bundle of a dual vector bundle is presented. This Lie algebroid is a new example of metrizable vector bundle. A new class of Hamilton spaces, called by use, generalized Hamilton (ρ,η)-space,…
The study of Chern numbers on vector bundles uses combinatorial methods to establish bounds and ordering.
problem Establishing bounds and ordering for Chern numbers on vector bundles.
method Combinatorial ideas to study Chern numbers on ample and numerically effective vector bundles.
result An effective lower bound for Chern numbers of ample vector bundles and reverse dominance ordering for nef vector bundles.
We construct a co-dimension completely non-holonomic sub-bundle on the Gromoll-Meyer exotic sphere based on its realization as a base space of a Sp(2)-principal bundle with the structure group Sp(1). The same method is valid for constructing a co-dimension 3 completely non-holonomic sub-bundle on the standard 7…
New method for decomposing manifolds into 1-handlebodies.
problem Decomposing manifolds into 1-handlebodies.
method Multisections of surface bundles and fiber bundles over the circle.
result Multisections exist for surface bundles and fiber bundles over the circle.
Let be a parabolic subgroup of a connected simply connected complex semisimple Lie group . Given a compact Kähler manifold , the dimensional reduction of -equivariant holomorphic vector bundles over was carried out by the first and third authors. This raises the question of dimensional reduct…
New proof classifies orbit closures in Hodge bundle.
problem Classifying -orbit closures in Hodge bundle.
method Using deformations of flat pairs of pants.
result Short proof of absolute period foliation classification.
Constructs a sheaf of Bargmann-Fock modules on Kähler manifolds.
problem Deformation quantization on Kähler manifolds.
method Extends Fedosov's method to Kähler manifolds with compatible Fedosov abelian connections.
result Explicit construction of sheaf of flat sections as a module over deformation quantization algebras.
Analyzes the moduli space of Higgs bundles to prove its quasi-projectivity.
problem Proving the quasi-projectivity of the moduli space of Higgs bundles.
method Uses analytic methods and the symplectic cut to construct a compactification.
result Proves the quasi-projectivity of the moduli space of Higgs bundles.
We consider various generalisations of the string class of a loop group bundle. The string class is the obstruction to lifting a bundle whose structure group is the loop group to one whose structure group is the Kac-Moody central extension of the loop group. We develop a notion of higher string classes for bundles…
Using the Morse-theoretic methods introduced by Hitchin, we prove that the moduli space of $\SO_0(1,n)$-Higgs bundles when is odd has two connected components.
In this paper, we propose a method of studying the modified Kahler-Ricci flow on projective bundles and give the explicit equation from the view point of symplectic geometry.
The paper constructs Einstein metrics on holomorphic bundles.
problem Finding complete conformally Kähler Einstein metrics on holomorphic bundles.
method Explicit momentum construction via ODE methods and Calabi ansatz.
result Non-trivial complete conformally Kähler Einstein metrics on certain holomorphic bundles are found.
The paper defines positivity for singular metrics on vector bundles and proves related theorems.
problem Positivity of singular Hermitian metrics for holomorphic vector bundles.
method The method of Berndtsson and Lempert, along with a Berndtsson-type positivity theorem for holomorphic vector bundles.
result Sharp extension theorem for holomorphic vector bundles.
We consider double plumbings of two disk bundles over spheres. We calculate the Heegaard-Floer homology with its absolute grading of the boundary of such a plumbing. Given a closed smooth 4-manifold and a suitable pair of classes in , we investigate when this pair of classes may be represented by a config…
We present a geometric interpretation of the integration-by-parts formula on an arbitrary vector bundle. As an application we give a new geometric formulation of higher-order variational calculus.
The aim of this paper is to study Seifert bundle structures on simply connected 5--manifolds. We classify all such 5--manifolds which admit a Seifert bundle structure, and in a few cases all Seifert bundle structures are also classified. These results are then used to construct positive Ricci curvature Einstein metrics…
This article is based on the methods developed in [AGG]. We construct a complex hyperbolic structure on a trivial disc bundle over a closed orientable surface (of genus 2) thus solving a long standing problem in complex hyperbolic geometry (see [Gol1, p. 583] and [Sch, p. 14]). This example answers also [Eli, Open …
We study the holomorphic vector bundles E over the twistor space Tw(M) of a compact simply connected hyperkähler manifold . We give a characterization of the semistability condition for E in terms of its restrictions to the holomorphic sections of the holomorphic twistor projection π:Tw(M)\rightarrow CP^1. It is sho…
We introduce logarithmic Picard algebroids, a natural class of Lie algebroids adapted to a simple normal crossings divisor on a smooth projective variety. We show that such algebroids are classified by a subspace of the de Rham cohomology of the divisor complement determined by its mixed Hodge structure. We then solve …
New method for quantizing symplectic manifolds with Lagrangian bundles.
problem Quantization of symplectic manifolds with Lagrangian bundles.
method A new construction of strict deformation quantization.
result Established a correspondence between differential operators and principal symbols.