The Geometry of Four-Manifolds

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ID: 297362
1990
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Abstract
Abstract The last ten years have seen rapid advances in the understanding of differentiable four-manifolds not least of which has been the discovery of new 'exotic' manifolds. These results have had far-reaching consequences in geometry, topology, and mathematical physics and have proved to be a mainspring of current mathematical research. This book provides a lucid and accessible account to the modern study of the geometry of four-manifolds. Consequently, it will form required reading for all those mathematicians and theoretical physicists whose research touches on this topic. Prerequisites are a firm grounding in differential geometry and topology as might be gained from the first year of a graduate course. The authors present both a thorough treatment of the main lines of these developments in four-manifold topology - notably the definition of new invariants of four-manifolds - and also a wide-ranging treatment of relevant topics from geometry and global analysis. All of the main theorems about Yang-Mills instantons on four-manifolds are proved in detail. On the geometric side, the book contains a new proof of the classification of instantons on the four-sphere, together with an extensive discussion of the differential geometry of holomorphic vector bundles. At the end of the book the different strands of the theory are brought together in the proofs of results which settle long-standing problems in four-manifolds topology and which are close to the frontiers of current research.
Reference Key
openalex_W614287400 Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors Simon Donaldson, P. B. Kronheimer
Journal Oxford University Press eBooks
Year 1990
DOI
10.1093/oso/9780198535539.001.0001
URL
https://doi.org/10.1093/oso/9780198535539.001.0001
Keywords Keywords not found

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