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Transactions of the American Mathematical Society

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Construction of a family of non-self-dual gauge fields

Author: Ignacio Sols
Journal: Trans. Amer. Math. Soc. 297 (1986), 505-508
MSC: Primary 14F05; Secondary 32L25, 81E13
MathSciNet review: 854080
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Abstract: Using the generalization of vector bundles by reflexive sheaves recently introduced by R. Hartshorne in [2] we construct a $ 15$-dimensional family of nontrivial complex gauge fields $ (U,E,\nabla )$ which are not self-dual nor anti-self-dual. ($ U$ is an affine neighborhood in $ {Q_4} = \operatorname{Gr} (2,{{\mathbf{C}}^4})$ of the stereographic compactification $ {S^4}$ of $ {\mathbb{R}^4}$, $ E$ is a vector bundle on $ U$ and $ \nabla $ is a connection on it whose curvature $ \phi $ satisfies the inequalities $ {}^{\ast}\phi \ne \phi $ and $ {}^{\ast}\phi \ne - \phi $.)

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Article copyright: © Copyright 1986 American Mathematical Society

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