Elements of combinatorial and differential topology
著者
書誌事項
Elements of combinatorial and differential topology
（Graduate studies in mathematics, v. 74）
American Mathematical Society, c2006
- タイトル別名
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Элементы комбинаторной и дифференциальной топологии
Ėlementy kombinatornoĭ i different︠s︡ialʹnoĭ topologii
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注記
Translation of: Элементы комбинаторной и дифференциальной топологии
Bibliography: p. 317-323
Includes index
内容説明・目次
内容説明
Modern topology uses very diverse methods. This book is devoted largely to methods of combinatorial topology, which reduce the study of topological spaces to investigations of their partitions into elementary sets, and to methods of differential topology, which deal with smooth manifolds and smooth maps. Many topological problems can be solved by using either of these two kinds of methods, combinatorial or differential. In such cases, both approaches are discussed. One of the main goals of this book is to advance as far as possible in the study of the properties of topological spaces (especially manifolds) without employing complicated techniques. This distinguishes it from the majority of other books on topology. The book contains many problems; almost all of them are supplied with hints or complete solutions.
目次
Basic definitions Graphs Topology in Euclidean space Topological spaces Two-dimensional surfaces, coverings, bundles, and homotopy groups Manifolds Fundamental groups Hints and solutions Bibliography Index.
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