Equivalences of smooth and continuous principal bundles with infinite-dimensional structure group

DOI10.1515/ADVGEOM.2009.032zbMath1184.22011arXivmath/0604142OpenAlexW3102785066MaRDI QIDQ3643535

Christoph Müller, Christoph Wockel

Publication date: 9 November 2009

Published in: advg (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0604142

zbMATH Keywords

infinite-dimensional Lie groupsmanifolds with cornerstwisted \(K\)-theorycontinuous principal bundlesequivalences of continuous and smooth principal bundlesnon-abelian Čech cohomologysmooth principal bundlessmoothing of continuous bundle equivalencessmoothing of continuous principal bundles

Mathematics Subject Classification ID

Infinite-dimensional Lie groups and their Lie algebras: general properties (22E65) Fiber bundles in algebraic topology (55R10) Smoothing in differential topology (57R10)

Related Items (16)

Constraints on families of smooth 4-manifolds from Bauer-Furuta invariants ⋮ Tautological classes of definite 4-manifolds ⋮ Smooth Homotopy of Infinite-Dimensional 𝐶^{∞}-Manifolds ⋮ Non-trivial smooth families of \(K3\) surfaces ⋮ On the Bauer–Furuta and Seiberg–Witten invariants of families of 4‐manifolds ⋮ A note on the Nielsen realization problem for 𝐾3 surfaces ⋮ On the generalization of Hilbert's fifth problem to transitive groupoids ⋮ Smooth homotopy of diffeological spaces: theory and applications to infinite-dimensional 𝐶^{∞}-manifolds ⋮ Unnamed Item ⋮ Obstruction classes of crossed modules of Lie algebroids and Lie groupoids linked to existence of principal bundles ⋮ Lie Groups of Bundle Automorphisms and Their Extensions ⋮ The Variations of Yang–Mills Lagrangian ⋮ Principal 2-bundles and their gauge 2-groups ⋮ Quasi-periodic paths and a string 2-group model from the free loop group ⋮ Rigidity of the mod 2 families Seiberg–Witten invariants and topology of families of spin 4-manifolds ⋮ Connections on central extensions, lifting gerbes, and finite-dimensional obstruction vanishing

Cites Work

• Analytische Faserungen über holomorph-vollständigen Räumen
• On a generalised Connes-Hochschild-Kostant-Rosenberg theorem
• Obstruction classes of crossed modules of Lie algebroids and Lie groupoids linked to existence of principal bundles
• Principal bundles and the Dixmier Douady class
• Twisted \(K\)-theory and \(K\)-theory of bundle gerbes
• The homotopy type of the unitary group of Hilbert space
• KK-theoretic duality for proper twisted actions
• Fundamentals of direct limit Lie theory

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