Integrability on direct limits of Banach manifolds

DOI10.5802/afst.1617zbMath1446.58002arXiv1408.3715OpenAlexW3019263967MaRDI QIDQ2183749

Fernand Pelletier, Patrick Cabau

Publication date: 27 May 2020

Published in: Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1408.3715

zbMATH Keywords

direct limitintegrable distributionalmost Lie bracketalmost Lie Banach algebroidanchor rangeKoszul connectionconvenient structures

Mathematics Subject Classification ID

Lie algebras of vector fields and related (super) algebras (17B66) Infinite-dimensional Lie groups and their Lie algebras: general properties (22E65) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with infinite-dimensional Lie algebras and other algebraic structures (37K30) Limits and colimits (products, sums, directed limits, pushouts, fiber products, equalizers, kernels, ends and coends, etc.) (18A30) Vector distributions (subbundles of the tangent bundles) (58A30) Infinite-dimensional manifolds (46T05)

Related Items (4)

Prolongations of convenient Lie algebroids ⋮ Completeness of Infinite-dimensional Lie Groups in Their Left Uniformity ⋮ Projective and Direct limits of Banach $G$ and tensor structures ⋮ An integrability criterion for a projective limit of Banach distributions

Cites Work

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• Integrability of weak distributions on Banach manifolds
• Second order tangent bundles of infinite dimensional manifolds
• Linear almost Poisson structures and Hamilton-Jacobi equation. Applications to nonholonomic mechanics
• A \(q\)-exponential statistical Banach manifold
• Inductive limits of topologies, their direct products, and problems related to algebraic structures
• Direct limits of infinite-dimensional Lie groups compared to direct limits in related categories
• Nonholonomic Lagrangian systems on Lie algebroids
• Manifolds, tensor analysis, and applications.
• Direct limit Lie groups and manifolds
• Connections on tangent bundles
• Banach Lie Algebroids
• ANALOGUES OF THE OBJECTS OF LIE GROUP THEORY FOR NONLINEAR POISSON BRACKETS
• Pontryagin Maximum Principle on Almost Lie Algebroids
• Fundamentals of direct limit Lie theory
• Integrability of Systems of Vectorfields
• Integrability of singular distributions on Banach manifolds
• Symplectic groupoids and Poisson manifolds
• Differential calculus on a Lie algebroid and Poisson manifolds
• Orbits of Families of Vector Fields and Integrability of Distributions
• Separation Axioms and Direct Limits
• Differentiability of a Function and of its Compositions with Functions of One Variable.
• Some Theorems on Direct Limits of Expanding Sequences of Manifolds.
• Algèbre commutative
• Weak Levi-Civita connection for the damped metric on the Riemannian path space and vanishing of Ricci tensor in adapted differential geometry

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