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Frames of Group Sets and Their Application in Bundle Theory [PDF]
Mathematics, 2020 We study fiber bundles where the fibers are not a group G but a free G-space with disjoint orbits. The fibers are then not torsors but disjoint unions of these; hence, we like to call them semi-torsors.
Eric J. Pap, Holger Waalkens
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Principal Bundle Structure of Matrix Manifolds
Mathematics, 2021 In this paper, we introduce a new geometric description of the manifolds of matrices of fixed rank. The starting point is a geometric description of the Grassmann manifold Gr(Rk) of linear subspaces of dimension ...
Marie Billaud-Friess +2 more
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Characteristic principal bundles [PDF]
Transactions of the American Mathematical Society, 1975 Characteristic principal bundles are the duals of commutative twisted group algebras. A principal bundle with locally compact second countable (Abelian) group and base space is characteristic iff it supports a continuous eigenfunction for almost every character measurably in the characters, also iff it is the quotient by Z of a principal E-bundle for ...
Harvey A. Smith
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Principal bundles on elliptic fibrations [PDF]
Asian Journal of Mathematics, 1997 A central role in recent investigations of the duality of F-theory and heterotic strings is played by the moduli of principal bundles, with various structure groups G, over an elliptically fibered Calabi-Yau manifold on which the heterotic theory is compactified.
Ron Donagi
+7 more sources
Can You Hear the Shape of a Market? Geometric Arbitrage and Spectral Theory
Axioms, 2021 Utilizing gauge symmetries, the Geometric Arbitrage Theory reformulates any asset model, allowing for arbitrage by means of a stochastic principal fibre bundle with a connection whose curvature measures the “instantaneous arbitrage capability”.
Simone Farinelli, Hideyuki Takada
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Power maps and principal bundles [PDF]
Proceedings of the American Mathematical Society, 1977 Let G be a path connected topological group. We investigate the integers m for which the mth power map on G extends to an overmap of principal G-bundles.
J. L. Noakes
+4 more sources
On connections on principal bundles
Arab Journal of Mathematical Sciences, 2017 A new construction of a universal connection was given in Biswas, Hurtubise and Stasheff (2012). The main aim here is to explain this construction. A theorem of Atiyah and Weil says that a holomorphic vector bundle E over a compact Riemann surface admits
Indranil Biswas
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Principal noncommutative torus bundles [PDF]
Proceedings of the London Mathematical Society, 2008 In this paper we study continuous bundles of C*-algebras which are non-commutative analogues of principal torus bundles. We show that all such bundles, although in general being very far away from being locally trivial bundles, are at least locally trivial with respect to a suitable bundle version of bivariant K-theory (denoted RKK-theory) due to ...
Echterhoff, Siegfried +2 more
arxiv +9 more sources
On synthetic interpretation of quantum principal bundles [PDF]
arXiv, 2009 Quantum principal bundles or principal comodule algebras are re-interpreted as principal bundles within a framework of Synthetic Noncommutative Differential Geometry. More specifically, the notion of a noncommutative principal bundle within a braided monoidal category is introduced and it is shown that a noncommutative principal bundle in the category ...
Brzeziński, Tomasz
arxiv +2 more sources
Stable Higgs bundles over positive principal elliptic fibrations
Complex Manifolds, 2018 Let M be a compact complex manifold of dimension at least three and Π : M → X a positive principal elliptic fibration, where X is a compact Kähler orbifold. Fix a preferred Hermitian metric on M.
Biswas Indranil +2 more
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