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Riemannian geometry and mathematical physics. Vector bundles and gauge theories. (English) Zbl 0849.53021
Cranny, Tim (ed.) et al., Instructional workshop on analysis and geometry, Canberra, Australia, January 23 - February 10, 1995. Part II: Geometric analysis. Canberra: Australian National University, Centre for Mathematics and its Applications. Proc. Cent. Math. Appl. Aust. Natl. Univ. 34(pt.2), 165-183 (1996).
The author considers the simplest theory of vector bundles where the vector space is a one-dimensional complex vector space, so-called line bundles. The definitions of line bundle, isomorphism of line bundles, section and transition functions are given in the introduction. In Section 2 the author explains such notions as connection, parallel transport, curvature and holonomy. In Section 3 the Chern classes are considered. The relation between the theory of vector bundles and gauge theories is briefly explained in Section 4.
For the entire collection see [Zbl 0844.00020].
Reviewer: M.Rahula (Tartu)
53C07 Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills)
53-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to differential geometry
81T13 Yang-Mills and other gauge theories in quantum field theory