The Weil algebra and the Van Est isomorphism

DOI10.5802/aif.2633zbMath1237.58021arXiv0901.0322OpenAlexW1664654057MaRDI QIDQ660439

Marius Crainic, Camilo Arias Abad

Publication date: 2 February 2012

Published in: Annales de l'Institut Fourier (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0901.0322

zbMATH Keywords

classifying spacesLie algebroidsequivariant cohomologyWeil algebraVan Est isomorphism

Mathematics Subject Classification ID

Poisson manifolds; Poisson groupoids and algebroids (53D17) Pseudogroups and differentiable groupoids (58H05) Homology of classifying spaces and characteristic classes in algebraic topology (55R40)

Related Items (21)

Linear and multiplicative 2-forms ⋮ Multisymplectic Geometry and Lie Groupoids ⋮ Poly-Poisson sigma models and their relational poly-symplectic groupoids ⋮ Local formulas for multiplicative forms ⋮ Shifted symplectic higher Lie groupoids and classifying spaces ⋮ Cohomologies of difference Lie groups and the van Est theorem ⋮ Hamiltonian Lie algebroids ⋮ Modules and representations up to homotopy of Lie \(n\)-algebroids ⋮ Lie theory and cohomology of relative Rota–Baxter operators ⋮ Multiplicative forms at the infinitesimal level ⋮ Momentum section on Courant algebroid and constrained Hamiltonian mechanics ⋮ Van Est isomorphism for homogeneous cochains ⋮ Differential forms with values in VB-groupoids and its Morita invariance ⋮ Lie groupoids and the Frölicher-Nijenhuis bracket ⋮ The holonomy groupoids of singularly foliated bundles ⋮ LIE ALGEBROIDS AS SPACES ⋮ Van Est differentiation and integration ⋮ Lie theory of multiplicative tensors ⋮ Homotopical algebra for Lie algebroids ⋮ Multiplicative forms and Spencer operators ⋮ Poly-symplectic groupoids and poly-Poisson structures

Cites Work

• Superconnections, Thom classes, and equivariant differential forms
• Foliated bundles and characteristic classes
• On the de Rham theory of certain classifying spaces
• On the Chern-Weil homomorphism and the continuous cohomology of Lie- groups
• Differentiable and algebroid cohomology, Van Est isomorphisms, and characteristic classes
• Integrability of Lie brackets
• Integration of twisted Dirac brackets
• Representations up to homotopy and Bott's spectral sequence for Lie groupoids
• Prequantization and Lie brackets
• Classifying spaces and spectral sequences
• Representations up to homotopy of Lie algebroids
• Symplectic groupoids and Poisson manifolds
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