3-manifolds
著者
書誌事項
3-manifolds
（Annals of mathematics studies, no. 86）
Princeton University Press, 1976
- : pbk
並立書誌 全1件
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3-manifolds / by John Hempel
BA31216289
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3-manifolds / by John Hempel
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注記
Bibliography: p. 185-191
Includes index
内容説明・目次
- 巻冊次
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ISBN 9780691081786
内容説明
This work treats the topological classification of 3-dimensional manifolds. Its unifying theme is the role of the fundamental group in determining the structure of a 3-manifold, and its purpose is to organize the subject around this theme. The reader is assumed to have some knowledge of algebraic topology and group theory.
The book begins with a treatment of the piecewise linear techniques which are used throughout, proceeds with a development of the basic tools (Heegard splittings, connected sum decompositions, and the loop and sphere theorems), and then turns to the two major questions: (1) which groups occur as (M) for some 3-manifold M? and (2) how closely does (M) reflect the topological structure of M? The bulk of the work considers various aspects of these questions and culminates with the description of a class of 3-manifolds which are completely determined by their fundamental group systems. One chapter discusses the still unsettled Poincare conjecture, and a final chapter examines some open questions which the author considers pertinent to further advances in the subject. The book contains several extensions of previously published results, some previously unpublished results, and many new proofs. It may be used as a text as "well as for reference purposes.
- 巻冊次
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: pbk ISBN 9780691081830
内容説明
This work treats the topological classification of 3-dimensional manifolds. Its unifying theme is the role of the fundamental group in determining the structure of a 3-manifold, and its purpose is to organize the subject around this theme. The reader is assumed to have some knowledge of algebraic topology and group theory. The book begins with a treatment of the piecewise linear techniques which are used throughout, proceeds with a development of the basic tools (Heegard splittings, connected sum decompositions, and the loop and sphere theorems), and then turns to the two major questions: (1) which groups occur as (M) for some 3-manifold M? and (2) how closely does (M) reflect the topological structure of M? The bulk of the work considers various aspects of these questions and culminates with the description of a class of 3-manifolds which are completely determined by their fundamental group systems. One chapter discusses the still unsettled Poincare conjecture, and a final chapter examines some open questions which the author considers pertinent to further advances in the subject.
The book contains several extensions of previously published results, some previously unpublished results, and many new proofs. It may be used as a text as "well as for reference purposes.
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