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Seiberg-Witten gauge theory. (English) Zbl 0954.53003
Texts and Readings in Mathematics. 17. New Delhi: Hindustan Book Agency. vii, 228 p. (1999).
This book is one of many introductions to Seiberg-Witten theory written shortly after the new equations were introduced in 1994. Since M. Marcolli is one of the people who worked on the Seiberg-Witten Floer theory, it is not surprising that this book has a large chapter on the Seiberg-Witten theory of 3-manifolds. This is one of the main differences between this book and other introductions to Seiberg-Witten theory. The other thing that sets this book apart is the extensive bibliography. M. Marcolli included every paper that she could find related to Seiberg-Witten gauge theory written between 1994 and 1998. The main bibliography was divided into eleven different parts and there are additional bibliographies after two of the chapters. This means that one must be careful to pick the correct reference number 11, when referred to reference 11. This book touches upon many different topics related to Seiberg-Witten theory. There is not room in the 200 pages to cover all the necessary details. The author’s intent was to provide a guide on ‘how to approach the study of Seiberg-Witten gauge theory’. This book will certainly give the reader a taste of many different topics and serve as a guide to the literature.

MSC:
53-02 Research exposition (monographs, survey articles) pertaining to differential geometry
57R57 Applications of global analysis to structures on manifolds
53D40 Symplectic aspects of Floer homology and cohomology
53C07 Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills)
53D45 Gromov-Witten invariants, quantum cohomology, Frobenius manifolds
57N10 Topology of general \(3\)-manifolds (MSC2010)
81T13 Yang-Mills and other gauge theories in quantum field theory
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