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From the reviews of the first edition: "This book exposes the beautiful confluence of deep techniques and ideas from mathematical physics and the topological study of the differentiable structure of compact four-dimensional manifolds, compact spaces locally modeled on the world in which we live and operate... The book is filled with insightful remarks, proofs, and contributions that have never before appeared in print. For anyone attempting to understand the work of Donaldson and the applications of gauge theories to four-dimensional topology, the book is a must." #Science#1 "I...

The workshop attracted more than 100 participants from various centres in Brazil, the US, Asia and Europe, ranging in experience from graduate students to leading experts in their field. The program covered topics in geometry, topology and physics, with special emphasis on harmonic maps, Kahler and contact geometry, gauge theory, low dimensional topology, and Seiberg-Witten theory. The contribution to this volume centre around a surprisingly deep interaction between quantum field theory from mathematical physics on the one hand and 4-dimensional topology on the other. Recent work by Witten...