Higher-dimensional Generalized Manifolds: Surgery and Constructions (EMS Series of Lectures in Mathematics) by Alberto Cavicchioli (PDF)

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A publication of the European Mathematical Society Generalized manifolds are a most fascinating subject to study. They were introduced in the 1930s, when topologists tried to detect topological manifolds among more general spaces. (This is now called the manifold recognition problem.) As such, generalized manifolds have served to enhance our understanding of the nature of genuine manifolds. However, it soon became more important to study the category of generalized manifolds itself. A breakthrough was made in the 1990s, when several topologists discovered a systematic way of constructing higher-dimensional generalized manifolds, based on advanced surgery techniques. In fact, the development of controlled surgery theory and the study of generalized manifolds developed in parallel. In this process, earlier studies of geometric surgery turned out to be very helpful. Generalized manifolds will continue to be an attractive subject to study, for there remain several unsolved fundamental problems. Moreover, they hold promise for new research, e.g. for finding appropriate structures on these spaces which could bring to light geometric (or even analytic) aspects of higher-dimensional generalized manifolds. This is the first book to systematically collect the most important material on higher-dimensional generalized manifolds and controlled surgery. It is self-contained and its extensive list of references reflects the historic development. The book is based on the authors’ graduate courses and seminars, as well as their talks given at various meetings, and is suitable for advanced graduate students and researchers in algebraic and geometric topology. A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society.

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Editorial Reviews: About the Author Alberto Cavicchioli: Università degli Studi di Modena e Reggio Emilia, Italy, Friedrich Hegenbarth: Univerità degli Studi di Milano, Italy, Du an Repov : University of Ljubljana, Slovenia A publication of the European Mathematical Society

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