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a review of Diffeological principal bundles and principal infinity bundles. by Minichiello, Emilio

a review of Diffeological principal bundles and principal infinity bundles. by Minichiello, Emilio
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Coverings in the Category of Principal Bundles

Russian Mathematics, 2021
The main object of this paper is to study regular coverings in the category of smooth principal bundles \(\xi = (E, p, B, G)\) with connected bases \(B\) and structural groups \(G\). A smooth principal bundle is a quadruple \(\xi = (E, p, B, G)\), where \(E\) and \(B\) are smooth manifolds, \(p\colon E \rightarrow B\) is a smooth mapping, and \(G\) is ...
E I Yakovlev
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The Atiyah bundle and connections on a principal bundle

Proceedings of the Indian Academy of Sciences: Mathematical Sciences, 2010
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Indranil Biswas
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Cohomology of Flat Principal Bundles

Proceedings of the Edinburgh Mathematical Society, 2018
AbstractWe invoke the classical fact that the algebra of bi-invariant forms on a compact connected Lie groupGis naturally isomorphic to the de Rham cohomologyH*dR(G) itself. Then, we show that when a flat connectionAexists on a principalG-bundleP, we may construct a homomorphismEA:H*dR(G)→H*dR(P), which eventually shows that the bundle satisfies a ...
Byun, Yanghyun, Kim, Joohee
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Principal Bundles

2020
This chapter examines principal bundles. Throughout the chapter, G will be a topological group. It then defines a principal G-bundle and provides a criterion for a map to be a principal G-bundle. This is followed by several examples of principal G-bundles.
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A covering property in principal bundles

2018
Summary: Let \(p:X\to B\) be a locally trivial principal \(G\)-bundle and \(\widetilde{p}:\widetilde{X}\to B\) be a locally trivial principal \(\widetilde{G}\)-bundle. In this paper, by using the structure of principal bundles according to transition functions, we show that \(\widetilde{G}\) is a covering group of \(G\) if and only if \(\widetilde{X}\)
Pakdaman, A., Attary, M.
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Stable Pairs and Principal Bundles

The Quarterly Journal of Mathematics, 2000
Let \(K\) be a connected compact Lie group, \(G\) its complexification, \(X\) a compact Kähler manifold, and \(E\to X\) be a principal holomorphic \(G\)-bundle over \(X\). Let \(W\) be a complex vector space and \(\rho: K\to U(W)\) a unitary representation of \(K\), which lifts to a representation \(\widetilde\rho\) of \(G\) and let \(V\to X\) be the ...
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Connections on principal prolongations of principal bundles

Differential Geometry and Its Applications, 2008
We study the principal connections on the r-th principal prolongation of a principal bundle by using the related Lie algebroids. We deduce that both approaches to the concept of torsion are naturally equivalent. Special attention is paid to the flow prolongation of connections.
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Curvature on a Principal Bundle

2020
This chapter examines curvature on a principal bundle. The curvature of a connection on a principal G-bundle is a g-valued 2-form that measures, in some sense, the deviation of the connection from the Maurer-Cartan connection on a product bundle. The Maurer-Cartan form Θ‎ on a Lie group G satisfies the Maurer-Cartan equation. Let M be a smooth manifold.
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Principal bundle groupoids, their gauge group and their nerve

Journal of Geometry and Physics, 2023
Alfonso Garmendia, Sylvie Paycha
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