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The Geometric Hopf Invariant and Surgery Theory / by Michael Crabb, Andrew Ranicki
(Springer Monographs in Mathematics. ISSN:21969922)
版 | 1st ed. 2017. |
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出版者 | (Cham : Springer International Publishing : Imprint: Springer) |
出版年 | 2017 |
本文言語 | 英語 |
大きさ | XVI, 397 p. 1 illus. in color : online resource |
著者標目 | *Crabb, Michael author Ranicki, Andrew author SpringerLink (Online service) |
件 名 | LCSH:Algebraic topology LCSH:Manifolds (Mathematics) FREE:Algebraic Topology FREE:Manifolds and Cell Complexes |
一般注記 | 1 The difference construction -- 2 Umkehr maps and inner product spaces -- 3 Stable homotopy theory -- 4 Z_2-equivariant homotopy and bordism theory -- 5 The geometric Hopf invariant -- 6 The double point theorem -- 7 The -equivariant geometric Hopf invariant -- 8 Surgery obstruction theory -- A The homotopy Umkehr map -- B Notes on Z2-bordism -- C The geometric Hopf invariant and double points (2010) -- References -- Index Written by leading experts in the field, this monograph provides homotopy theoretic foundations for surgery theory on higher-dimensional manifolds. Presenting classical ideas in a modern framework, the authors carefully highlight how their results relate to (and generalize) existing results in the literature. The central result of the book expresses algebraic surgery theory in terms of the geometric Hopf invariant, a construction in stable homotopy theory which captures the double points of immersions. Many illustrative examples and applications of the abstract results are included in the book, making it of wide interest to topologists. Serving as a valuable reference, this work is aimed at graduate students and researchers interested in understanding how the algebraic and geometric topology fit together in the surgery theory of manifolds. It is the only book providing such a wide-ranging historical approach to the Hopf invariant, double points and surgery theory, with manyresults old and new. HTTP:URL=https://doi.org/10.1007/978-3-319-71306-9 |
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電子ブック | 配架場所 | 資料種別 | 巻 次 | 請求記号 | 状 態 | 予約 | コメント | ISBN | 刷 年 | 利用注記 | 指定図書 | 登録番号 |
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電子ブック | オンライン | 電子ブック |
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Springer eBooks | 9783319713069 |
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EB00234450 |
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データ種別 | 電子ブック |
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分 類 | LCC:QA612-612.8 DC23:514.2 |
書誌ID | 4000116886 |
ISBN | 9783319713069 |
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※2017年9月4日以降