Gauge Theory in Higher Dimensions (Colóquio Brasileiro de Matemática)
Gauge Theory in Higher Dimensions (Colóquio Brasileiro de Matemática) by IMPA
English | April 27, 2021 | ISBN: 8524404809 | 197 pages | PDF | 1.46 Mb
English | April 27, 2021 | ISBN: 8524404809 | 197 pages | PDF | 1.46 Mb
This book is an introduction to gauge theory in dimensions greater than 4. It is organised as a reader's guide to Gang Tian's landmark article Gauge theory and calibrated geometry, Ia, published in the Annals of Mathematics in 2000. Tian carried out to substantial lengths the programme outlined by Simon Donaldson and Richard Thomas in their seminal paper, by extending the fundamental notion of instanton in Yang-Mills theory to higher dimensional special geometries. Moreover, his bubbling theorem relates instanton compactness to the theory of calibrated submanifolds. This work expresses our admiration for all of these key authors.The text is aimed at graduate students and advanced undergraduates, as well as specialists in other areas of Mathematics and Physics, with an interest in modern Differential Geometry. We adopt a fast-paced but self-contained exposition of the background on connections and curvature on bundles, special geometric structures, analysis on manifolds and geometric measure theory, alongside the proof of Tian's bubbling theorem. We also highlight some links with other important works in contemporary Geometry and Topology.
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