Formulates 2-connections and gauge transformations for principal 2-bundles using an operational framework based on crossed modules and derived Lie groups.
Principal 2-bundles and their gauge 2-groups
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abstract
In this paper we introduce principal 2-bundles and show how they are classified by non-abelian Cech cohomology. Moreover, we show that their gauge 2-groups can be described by 2-group-valued functors, much like in classical bundle theory. Using this, we show that, under some mild requirements, these gauge 2-groups possess a natural smooth structure. In the last section we provide some explicit examples.
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UNVERDICTED 3representative citing papers
A spherical Milnor space construction yields projective quotients and double quotients that encode Z2-twisted principal bundles and obstruction classes in low-degree cohomology.
Introduces diffeological spherical and projective Milnor classifying spaces with compatible Riemannian metrics, differential calculus, Hodge theory, and Dirac operators in infinite-dimensional geometry.
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Operational total space theory of principal 2-bundles II: 2-connections and 1- and 2--gauge transformations
Formulates 2-connections and gauge transformations for principal 2-bundles using an operational framework based on crossed modules and derived Lie groups.
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Spherical Milnor Spaces II: Projective Quotients and Higher Topological Structures
A spherical Milnor space construction yields projective quotients and double quotients that encode Z2-twisted principal bundles and obstruction classes in low-degree cohomology.
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On spherical Milnor Classifying Spaces I: differential geometry
Introduces diffeological spherical and projective Milnor classifying spaces with compatible Riemannian metrics, differential calculus, Hodge theory, and Dirac operators in infinite-dimensional geometry.