The previous 20 years have introduced explosive development in 4-manifold thought. Many books are presently showing that method the subject from viewpoints resembling gauge idea or algebraic geometry. This quantity, even if, deals an exposition from a topological viewpoint. It bridges the space to different disciplines and offers classical yet very important topological innovations that experience no longer formerly seemed within the literature. half I of the textual content offers the fundamentals of the speculation on the second-year graduate point and provides an summary of present examine. half II is dedicated to an exposition of Kirby calculus, or handlebody thought on 4-manifolds. it really is either simple and entire. half III deals intensive a huge variety of subject matters from present 4-manifold study. themes contain branched coverings and the geography of complicated surfaces, elliptic and Lefschetz fibrations, $h$-cobordisms, symplectic 4-manifolds, and Stein surfaces. purposes are featured, and there are over three hundred illustrations and various routines with recommendations within the booklet.
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