The earlier twenty years have introduced explosive progress in 4-manifold idea. Many books are at present showing that process the subject from viewpoints similar to gauge conception or algebraic geometry. This quantity, although, bargains an exposition from a topological perspective. It bridges the space to different disciplines and provides classical yet vital topological suggestions that experience no longer formerly seemed within the literature. half I of the textual content provides the fundamentals of the speculation on the second-year graduate point and gives an outline of present learn. half II is dedicated to an exposition of Kirby calculus, or handlebody idea on 4-manifolds. it really is either uncomplicated and accomplished. half III bargains intensive a wide variety of themes from present 4-manifold study. subject matters contain branched coverings and the geography of complicated surfaces, elliptic and Lefschetz fibrations, $h$-cobordisms, symplectic 4-manifolds, and Stein surfaces. functions are featured, and there are over three hundred illustrations and various routines with recommendations within the booklet.
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