Results 291 to 300 of about 198,779 (330)
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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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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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Cohomology of Flat Principal Bundles
Proceedings of the Edinburgh Mathematical Society, 2018AbstractWe 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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A covering property in principal bundles
2018Summary: 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, 2000Let \(K\) 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, 2008We 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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Autophagy and autophagy-related pathways in cancer
Nature Reviews Molecular Cell Biology, 2023, Kevin M Ryan
exaly
2002
A very important theorem in the geometry of contact manifolds, and the start of the modern theory, is the Boothby–Wang theorem, which states that a compact regular contact manifold is a principal circle bundle over a symplectic manifold of integral class. We will prove this result in Section 3.3.
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A very important theorem in the geometry of contact manifolds, and the start of the modern theory, is the Boothby–Wang theorem, which states that a compact regular contact manifold is a principal circle bundle over a symplectic manifold of integral class. We will prove this result in Section 3.3.
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Connections on Principal Bundles
2015The topic of this chapter has become standard in modern treatments of differential geometry. The very words of the title have even been incorporated into part of a common cliche: Gauge theory is a connection on a principal bundle. We will come back to this relation between physics and geometry in Chapter 14 But just on the geometry side there has been ...
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