Principal 2-bundles and their gauge 2-groups

DOI10.1515/FORM.2011.020zbMath1232.55013arXiv0803.3692MaRDI QIDQ3006395

Christoph Wockel

Publication date: 14 June 2011

Published in: Forum Mathematicum (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0803.3692

zbMATH Keywords

Lie groupoidMorita equivalenceprincipal bundlecategorical Lie group

Mathematics Subject Classification ID

Yang-Mills and other gauge theories in quantum field theory (81T13) Infinite-dimensional Lie groups and their Lie algebras: general properties (22E65) Generalizations of fiber spaces and bundles in algebraic topology (55R65)

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Cites Work

• Coherence for categories with group structure: An alternative approach
• Faisceaux algébriques cohérents
• Obstruction classes of crossed modules of Lie algebroids and Lie groupoids linked to existence of principal bundles
• Towards a Lie theory of locally convex groups
• Non-abelian differentiable gerbes
• Central extensions of groups of sections
• Kohaerenz in Kategorien mit Gruppenstruktur
• Spaces with finitely many non-trivial homotopy groups
• The geometry of degree-four characteristic classes and of line bundles on loop spaces. I
• Lie group structures on quotient groups and universal complexifications for infinite-dimensional Lie groups
• Lie group structures on symmetry groups of principal bundles
• Central extensions of gauge transformation groups of higher Abelian gerbes
• Nonabelian bundle gerbes, their differential geometry and gauge theory
• Differential geometry of gerbes
• Note on a previous paper entitled 'On adding relations to homotopy groups'
• Fundamentals of direct limit Lie theory
• Integrating -algebras
• Equivalences of smooth and continuous principal bundles with infinite-dimensional structure group
• Sur La Cohomologie Non Abelienne I (Dimension Deux)
• Non-Abelian Extensions of Topological Lie Algebras