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4-Manifolds and Kirby Calculus, Paperback / softback Book


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.


  • Format: Paperback / softback
  • Pages: 558 pages, 300+ illustrations
  • Publisher: American Mathematical Society
  • Publication Date:
  • Category: Topology
  • ISBN: 9780821809945



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