Results 11 to 20 of about 104,879 (300)
A geometric approach to discrete connections on principal bundles
Journal of Geometric Mechanics, 2013 This work revisits, from a geometric perspective, the notion of discrete connection on a principal bundle, introduced by M. Leok, J. Marsden and A. Weinstein. It provides precise definitions of discrete connection, discrete connection form and discrete horizontal lift and studies some of their basic properties and relationships. An existence result for
Javier Fernández +3 more
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Connections on a parabolic principal bundle, II [PDF]
Canadian Mathematical Bulletin, 2007 AbstractIn Connections on a parabolic principal bundle over a curve, I we defined connections on a parabolic principal bundle. While connections on usual principal bundles are defined as splittings of the Atiyah exact sequence, it was noted in the above article that the Atiyah exact sequence does not generalize to the parabolic principal bundles.
Indranil Biswas
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Functoriality of Principal Bundles and Connections [PDF]
, 2019 Perhaps the most important contribution of gauge theory to general mathematics is to point out the importance of association functors. Emphasizing category theory we characterize association functors by two of their natural properties and use this characterization to establish an equivalence between the category of principal bundles and a suitably ...
Gustavo Amilcar Saldaña Moncada +1 more
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Discrete connections on principal bundles: The discrete Atiyah sequence [PDF]
Journal of Geometry and Physics, 2021 In this work we study discrete analogues of an exact sequence of vector bundles introduced by M. Atiyah in 1957, associated to any smooth principal $G$-bundle $π:Q\rightarrow Q/G$. In the original setting, the splittings of the exact sequence correspond to connections on the principal bundle $π$.
Javier Fernández +2 more
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A categorical equivalence between generalized holonomy maps on a connected manifold and principal connections on bundles over that manifold [PDF]
, 2016 A classic result in the foundations of Yang-Mills theory, due to J. W. Barrett ["Holonomy and Path Structures in General Relativity and Yang-Mills Theory." Int. J. Th. Phys.
Sarita Rosenstock, James Owen Weatherall
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Criterion for connections on principal bundles over a pointed Riemann surface
Complex Manifolds, 2017 We investigate connections, and more generally logarithmic connections, on holomorphic principal bundles over a compact connected Riemann surface.
Biswas Indranil
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Principal bundles and connections modelled by Lie group bundles [PDF]
Geometriae Dedicata, 2022 AbstractIn this work, generalized principal bundles modelled by Lie group bundle actions are investigated. In particular, the definition of equivariant connections in these bundles, associated to Lie group bundle connections, is provided, together with the analysis of their existence and their main properties. The final part gives some examples.
Marco Castrillón López +1 more
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A remark on “Connections and Higgs fields on a principal bundle” [PDF]
Annals of Global Analysis and Geometry, 2011 We show that a unipotent vector bundle on a non-Kaehler compact complex manifold does not admit a flat holomorphic connection in general. We also construct examples of topologically trivial stable vector bundle on compact Gauduchon manifold that does not admit any unitary flat connection.
Indranil Biswas +3 more
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Root stacks, principal bundles and connections [PDF]
Bulletin des Sciences Mathématiques, 2012 We investigate principal bundles over a root stack. In case of dimension one, we generalize the criterion of Weil and Atiyah for a principal bundle to have an algebraic connection.
Indranil Biswas +2 more
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Principal Bundles, Connections and BRST Cohomology [PDF]
, 1994 31 pages ...
Hugo Garcı́a-Compeán +3 more
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