Existence and rigidity results for lifts in Carnot groups.
problem Existence and properties of lifts for maps between Carnot groups.
method Use central extensions to define lifts and prove existence and rigidity results for Lipschitz, Sobolev, and quasiconformal maps.
result Quasiconformal maps admit contact lifts that are bi-Lipschitz.
Study lift metrics and connections on tangent bundles of Riemannian manifolds.
problem Investigate geometric properties of tangent bundles and their lifts.
method Analyze lift metrics and connections on TM of (M,g), and study statistical and Codazzi couples. result Prove a result on 1-Stein and Osserman structures on TM. Abstract: Counterexamples found for lifting Hamiltonian and contact isotopies.
problem Lifting properties of Hamiltonian and contact isotopies.
method Constructing counterexamples.
result Found counterexamples to lifting properties.
In this paper, we define a complete lift for semisprays. If S is a semispray on a manifold M, its complete lift is a new semispray Sc on TM. The motivation for this lift is two-fold: First, geodesics for Sc correspond to the Jacobi fields for S, and second, this complete lift generalizes and unifies previ…
Unified approach to constructing integrable systems using Stäckel lifts.
problem Constructing new integrable Hamiltonian systems.
method Generalized Stäckel geometry and Haantjes structure.
result Hamiltonian systems with momentum-dependent Stäckel matrices exhibit symplectic-Haantjes structures.
Geometric structures are lifted to higher tangent bundles preserving statistical properties.
problem Lifting statistical structures to higher tangent bundles while maintaining their properties.
method Natural lifts of geometric objects and potentials to higher tangent bundles, preserving statistical manifold structures.
result Lifted statistical structures on higher tangent bundles maintain pseudo-Riemannian metrics and are again statistical manifolds.
The article classifies liftings of connections on differential manifolds for geodesic modeling.
problem Classifying liftings of connections on differential manifolds.
method Liftings of connections on frame bundles, induced and adjust liftings.
result Developed a method for geodesic modeling of differential equations.
Maps can be embedded in higher dimensions if they lift to embeddings in product spaces.
problem Embedding maps in higher dimensions without self-intersections.
method Lifting maps to embeddings in product spaces.
result Maps can be embedded in higher dimensions if they lift to embeddings in product spaces.
In the present paper, we study complete and vertical lifts of tensor fields from a smooth manifold M to its Weil bundle TAM defined by a Frobenius Weil algebra A. For a Poisson manifold (M,w), we show that the complete lift wC and the vertical lift wV of the Poisson tensor w are Poisson tensors on $T^…
Study lifts plane mappings to Heisenberg group.
problem Contact quasiconformal mappings in hyperbolic Heisenberg group.
method Lifting Theorem for symplectic mappings.
result Symplectic mappings lifted to Heisenberg group.
The paper lifts spherical Morse functions to immersions and embeddings.
problem Lifting spherical Morse functions to other maps.
method New methods to lift to special generic maps with non-positive codimensions.
result Constructs most lifts to special generic maps.
In this paper we continue to study equivariant pencil liftings and differential operators on the algebra of densities. We emphasize the role that the geometry of the extended manifold plays. Firstly we consider basic examples. We give a projective line of diff(M)-equivariant pencil liftings for first order operators,…
This paper studies surfaces with a special lift property.
problem Geometry of surfaces with a specific lift property.
method Generalizes previous results by Bernstein and Tinaglia.
result Leaves of minimal laminations satisfy the generalised simple lift property.
Study covers of sphere with homeomorphisms lifting property.
problem Finite abelian covers of sphere with lifting homeomorphisms.
method Completely determined covers with specific lifting property.
result Properties of finite abelian covers with lifting homeomorphisms.
Researchers lift spectral ζ-invariants to coverings using defect formulae.
problem Lifting spectral ζ-invariants to coverings of closed manifolds.
method Using lifted defect formulae and Wodzicki residues.
result Derived integrals of Pontryagin and Chern forms for certain lifted spectral ζ-invariants.
The paper constructs Sasakian lifts from Kähler manifolds and studies their properties.
problem Constructing Sasakian structures from Kähler manifolds and analyzing their geometric properties.
method Local construction of Sasakian manifolds from Kähler base using vector field operations.
result Existence and properties of α-Sasakian Ricci solitons in Sasakian lifts. The paper discusses symplectic lifts for actions on Lagrangian fibrations.
problem Understanding symplectic lifts for actions on Lagrangian fibrations.
method Describes symplectic cotangent lifts in terms of 1-cocycles and generalizes to complete Lagrangian fibrations.
result Symplectic lifts of actions for complete Lagrangian fibrations are understood in terms of cohomology.
New quantum code lacks sparse lift.
problem Existence of sparse lifts for quantum codes.
method Constructed a sparse Z2 chain complex without a sparse lift. result Found a quantum code without a sparse lift.
Criteria for lifting manifold diffeomorphisms to vector bundle automorphisms.
problem Lifting diffeomorphisms to vector bundles.
method Criteria for lifting diffeomorphisms to linear automorphisms of vector bundles.
result Criteria for lifting diffeomorphisms to linear automorphisms of vector bundles.
Characterizes sphere covers with lifted homeomorphisms.
problem Characterizing sphere covers with lifted homeomorphisms.
method Characterization through cyclic branched covers and homeomorphisms.
result Every homeomorphism of the sphere lifts to a homeomorphism of the covering surface in these cases.
This paper extends braid lifting to coloured braid groupoids for all simple disc covers.
problem Lifting braids to homeomorphisms on branched covers of the disc.
method Defines a map from a coloured braid groupoid to a mapping class groupoid for all simple covers of the disc.
result Characterizes the lift of every coloured braid, recovering classical lifting on liftable braids.
Simple lifts of non-simple curves on surfaces.
problem Finding simple lifts of non-simple closed curves on surfaces.
method Constructing finite covers and curves on surfaces.
result Explicit non-simple closed curves with simple lifts on degree n covers.
Defines lift of partial cohomological field theories and finds new bi-Hamiltonian structures.
problem Non-semisimple homogeneous partial cohomological field theories and their integrable systems.
method Lift procedure for Frobenius algebras and local polyvector fields.
result Examples of non-semisimple homogeneous partial cohomological field theories with second Hamiltonian structure.
Curious examples of lifting spaces not as inverse limits of covering spaces.
problem Understanding inverse limits of covering spaces and their properties.
method Analyzing inverse limits of sequences of covering spaces over a given space.
result Presented examples of lifting spaces that cannot be obtained as inverse limits of covering spaces.
We construct some lift of an almost complex structure to the cotangent bundle, using a connection on the base manifold. This generalizes the complete lift defined by I.Sato and the horizontal lift introduced by K.Yano and S.Ishihara. We study some geometric properties of this lift and its compatibility with symplectic …
Fenchel lifted networks improve neural network training without performance loss.
problem The difficulty and non-convexity of training deep neural networks.
method Introduces Fenchel lifted networks that represent activation functions as biconvex constraints and uses Lagrange Multipliers to create a lower bound of the training problem.
result Fenchel lifted networks match or outperform traditional neural networks in performance.
In Finsler geometry the complete lift vector fields have distinguished geometric significance. For example a vector field on a Finsler manifold is said to be conformal if its complete lift is conformal in usual sense. In this work we define a new Riemannian or Pseudo-Riemannian metric on TM derived from a Finsler metri…
Proves harmonicity equivalence on manifold metrics.
problem Harmonicity of metrics on pseudo-Riemannian manifolds.
method Equivalence of harmonicity on manifold metrics and their lifts.
result Harmonicity of a metric is equivalent to its lifts' harmonicity.
The Eisenhart lift connects Hamiltonian systems to geodesics in pp-wave spacetimes.
problem Studying the stability and dynamics of Hamiltonian systems.
method Eisenhart lift to pp-wave spacetimes and conformal classes of ODEs.
result Existence of a constant of the motion generalizing conservation of energy.
Pseudo-Anosov maps on nonorientable surfaces have vanishing SAF invariant.
problem Understanding pseudo-Anosov maps on nonorientable surfaces.
method Analyzing the SAF invariant of pseudo-Anosov maps.
result Lifts of pseudo-Anosov homeomorphisms on nonorientable surfaces have vanishing SAF invariant.
Survey of twistor lifts of surfaces in 4-dimensional spaces.
problem Understanding the properties of surfaces in 4-dimensional Euclidean space.
method Definitions of Gauss maps and twistor lifts using orthogonal complex structures.
result Holomorphicity and isotropicity of minimal surfaces in E4. New method tightens convex relaxations for permutation matrix problems without lifting.
problem Optimizing quadratic problems over permutation matrices.
method Lifting-free convex relaxation approach.
result Proves at least as tight as existing methods and performs better experimentally.
Study of lifting maps in branched covers of 3-manifolds, showing non-injectivity.
problem Injectivity of lifting maps in branched covers of 3-manifolds.
method Analysis of branched covers and mapping class groups.
result Lifting map is generally not injective for most regular branched covers of 3-manifolds.
Develops a new bidding system to maximize advertiser profit.
problem Inaccurate prediction of ad lift-effect due to biased log data.
method Unbiased Lift-based Bidding System that predicts lift-effect from biased log data.
result Demonstrates superior and practical high-performing lift-based bidding strategy.
Investigates fundamental groups and path lifting for algebraic varieties.
problem Understand fundamental groups and path lifting properties of algebraic varieties.
method Analyzes three fundamental questions about fundamental groups of algebraic varieties.
result Identifies conditions for surjectivity on fundamental groups and path lifting properties.
We construct a connection and a curving on a bundle gerbe associated with lifting a structure group of a principal bundle to a central extension. The construction is based on certain structures on the bundle, i.e. connections and splittings. The Deligne cohomology class of the lifting bundle gerbe with the connection a…
Develops a new algebraic framework for differential geometry of infinite dimensional spaces.
problem Creating a differential geometry for infinite dimensional spaces without topology or local coordinates.
method Introduces a general algebraic framework for lifted geometry applicable to various infinite dimensional spaces.
result Stokes' Theorem appears as a form of differentiability in the lifted geometry of spaces of submanifolds.
We show that one can lift locally real analytic curves from the orbit space of a compact Lie group representation, and that one can lift smooth curves even globally, but under an assumption.
Researchers lift knot coloring polynomial to Habiro ring.
problem Lifting colored Jones polynomial of knots to Habiro ring.
method Introduced new Habiro ring and map, used Alexander polynomial.
result Existence of loop expansion at roots of unity confirmed.
We show the total space of the canonical line bundle L of a Kahler-Einstein manifold Xn supports integrable SU(n+1) structures, or Calabi-Yau structures. The canonical real line bundle L⊂L over a minimal Lagrangian submanifold M⊂X is calibrated in this setting and hence can …
We analyze variational inference for highly symmetric graphical models such as those arising from first-order probabilistic models. We first show that for these graphical models, the tree-reweighted variational objective lends itself to a compact lifted formulation which can be solved much more efficiently than the sta…
Study proves Hecke lifting conjecture for torus knots and verifies it for any framed knots.
problem Integrality structure of framed knots' quantum invariants.
method Explicit formulas of colored HOMFLY-PT invariants of torus knots, verified in a limit form for any framed knots.
result Proves Hecke lifting conjecture for torus knots and verifies it for any framed knots.
Lifting speeds up ADMM convergence for quadratic objectives.
problem Slower convergence of ADMM for quadratic objectives.
method Distributed ADMM as a lifting of Gradient Descent.
result ADMM converges faster with optimal parameter tuning.
Lie groupoids and their orbit spaces are linked through equivalence classes.
problem Understanding the relationship between Lie groupoids and their orbit spaces.
method Introducing lift-complete Lie groupoids and showing equivalence between categories.
result Morita equivalence class of a lift-complete Lie groupoid is determined by its orbit space.
Develops a lifting theory for exponential maps in semi-Riemannian geometry.
problem Overcoming singularities in exponential maps to prove geodesic connectivity.
method Lifting theory for semi-Riemannian manifolds with path-continuation property.
result General path-lifting theorem extending globally under certain conditions.
Classifies connections on central extensions and finds vanishing obstruction classes.
problem Classifying connections on central extensions of Lie groups.
method Introducing a new connective structure on the lifting gerbe and proving a vanishing result for Neeb's obstruction classes.
result Admissible connections correspond to parallel trivializations of the lifting gerbe and vanishing obstruction classes.
Introduces new construction for Courant algebroids and curved structures.
problem Understanding and classifying Courant algebroids and their lifts.
method Introduces Courant algebroid lift and curved Courant algebroids, establishing connections to various geometric structures.
result Established a classification of exact curved Courant algebroids and related connections to various geometric structures.
Study metallic structures on tangent bundles with lifts and integrability.
problem Integrability and lifts of metallic structures on tangent bundles.
method Complete and horizontal lifts with respect to almost product structure, fundamental formulae establishment.
result Behavior of metallic structure cross-sections in tangent bundle TM.