The past two decades have brought explosive growth in 4-manifold theory. Many books are currently appearing that approach the topic from viewpoints such as gauge theory or algebraic geometry. This volume, however, offers an exposition from a topological point of view. It bridges the gap to other disciplines and presents classical but important topological techniques that have not previously appeared in the literature. Part I of the text presents the basics of the theory at the second-year graduate level and offers an overview of current research.Part II is devoted to an exposition of Kirby calculus, or handle body theory on 4-manifolds. It is both elementary and comprehensive. Part III offers in depth a broad range of topics from current 4-manifold research. Topics include branched coverings and the geography of complex surfaces, elliptic and Lefschetz fibrations, $h$-cobordisms, symplectic 4-manifolds, and Stein surfaces. Applications are featured, and there are over 300 illustrations and numerous exercises with solutions in the book.
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978-0-8218-0994-5 (9780821809945)
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Schweitzer Klassifikation
4-manifolds: Introduction Surfaces in 4-manifolds Complex surfaces Kirby calculus: Handelbodies and Kirby diagrams Kirby calculus More examples Applications: Branched covers and resolutions Elliptic and Lefschetz fibrations Cobordisms, $h$-cobordisms and exotic ${\mathbb{R}}^{4,}$s Symplectic 4-manifolds Stein surfaces Appendices: Solutions Notation, important figures Bibliography Index.
