Surgery Theory: Foundations
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Surgery theory was developed to carry out the so-called Surgery Program, a basic strategy to decide whether two closed manifolds are homeomorphic or diffeomorphic. This book provides a detailed explanation of all the ingredients necessary for carrying out the surgery program, as well as an in-depth discussion of the obstructions that arise. The components include the surgery step, the surgery obstruction groups, surgery obstructions, and the surgery exact sequence. This machinery is applied to homotopy spheres, the classification of certain fake spaces, and topological rigidity. The book also offers a detailed description of Ranicki's chain complex version, complete with a proof of its equivalence to the classical approach developed by Browder, Novikov, Sullivan, and Wall.
This book has been written for learning surgery theory and includes numerous exercises. With full proofs and detailed explanations, it also provides an invaluable reference for working mathematicians. Each chapter has been designed to be largely self-contained and includes a guide to help readers navigate the material, making the book highly suitable for lecture courses, seminars, and reading courses.
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Tibor Macko is an associate professor of mathematics at the Comenius University and a research fellow at the Slovak Academy of Sciences, both in Bratislava. He obtained his PhD in 2004 from the University of Aberdeen and was later apostdoc at MPI in Bonn and at the universities at Münster and Bonn before returning to his native Slovakia. He is an author or a coauthor of more than a dozen papers on topology of manifolds.
