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The geometry of degree-four characteristic classes and of line bundles on loop spaces I
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This article is published in Duke Mathematical Journal.The article was published on 1994-09-01. It has received 128 citations till now. The article focuses on the topics: Splitting principle & Vector bundle.read more
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Chern-Simons theory with finite gauge group
Daniel S. Freed,Frank Quinn +1 more
TL;DR: In this article, a 2+1 dimensional gauge field theory with finite gauge group was constructed, where the path integral reduces to a finite sum and there are no analytic problems with the quantization.
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Higher algebraic structures and quantization
TL;DR: In this paper, the authors derived quasi-quantum groups in 2+1 dimensional topological field theory directly from the classical action and the path integral, and then constructed a generalized path integral which ind+1 dimensions reduces to the standard one and ind dimensions reproduces the quantum Hilbert space.
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An invitation to higher gauge theory
John C. Baez,John Huerta +1 more
TL;DR: In this article, the authors describe parallel transport for particles and strings in terms of 2-connections on 2-bundles, which is a generalization of higher gauge theory.
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Bundle Gerbes: Stable Isomorphism and Local Theory
TL;DR: The notion of stable isomorphism of bundle gerbes is considered in this article, which has the consequence that the stable isomorphic classes of the bundle gerbe over a manifold M are in bijective correspondence with H3(M, ℤ).
Journal ArticleDOI
An Invitation to Higher Gauge Theory
John C. Baez,John Huerta +1 more
TL;DR: In this paper, the authors describe parallel transport for particles and strings in terms of 2-connections on 2-bundles, which is a generalization of higher gauge theory.
References
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Quantum field theory and the Jones polynomial
TL;DR: In this paper, it was shown that 2+1 dimensional quantum Yang-Mills theory with an action consisting purely of the Chern-Simons term is exactly soluble and gave a natural framework for understanding the Jones polynomial of knot theory in three dimensional terms.
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The Yang-Mills equations over Riemann surfaces
Michael Atiyah,Raoul Bott +1 more
TL;DR: In this article, the Yang-Mills functional over a Riemann surface is studied from the point of view of Morse theory, and the main result is that this is a perfect 9 functional provided due account is taken of its gauge symmetry.
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Théorie de Hodge : III
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Stable and unitary vector bundles on a compact Riemann surface
M. S. Narasimhan,C. S. Seshadri +1 more
TL;DR: In this article, it was shown that on the space of isomorphic classes of unitary vector bundles on X of a given rank, there is a natural structure of a normal projective variety (Theorem 8.1).