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Boundedly Controlled Topology : Foundations of Algebraic Topology and Simple Homotopy Theory / by Douglas R. Anderson, Hans J. Munkholm
(Lecture Notes in Mathematics. ISSN:16179692 ; 1323)
版 | 1st ed. 1988. |
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出版者 | (Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer) |
出版年 | 1988 |
大きさ | XIV, 310 p : online resource |
著者標目 | *Anderson, Douglas R author Munkholm, Hans J author SpringerLink (Online service) |
件 名 | LCSH:Algebraic topology FREE:Algebraic Topology |
一般注記 | Category theoretic foundations -- The algebraic topology of boundedly controlled spaces -- The geometric, boundedly controlled whitehead group -- Free and projective rpg modules the algebraic whitehead groups of rpg -- The isomorphism between the geometric and algebraic whitehead groups -- Boundedly controlled manifolds and the s-cobordism theorem -- Toward computations Several recent investigations have focused attention on spaces and manifolds which are non-compact but where the problems studied have some kind of "control near infinity". This monograph introduces the category of spaces that are "boundedly controlled" over the (usually non-compact) metric space Z. It sets out to develop the algebraic and geometric tools needed to formulate and to prove boundedly controlled analogues of many of the standard results of algebraic topology and simple homotopy theory. One of the themes of the book is to show that in many cases the proof of a standard result can be easily adapted to prove the boundedly controlled analogue and to provide the details, often omitted in other treatments, of this adaptation. For this reason, the book does not require of the reader an extensive background. In the last chapter it is shown that special cases of the boundedly controlled Whitehead group are strongly related to lower K-theoretic groups, and the boundedly controlled theory is compared to Siebenmann's proper simple homotopy theory when Z = IR or IR2 HTTP:URL=https://doi.org/10.1007/BFb0079806 |
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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 | 9783540392491 |
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EB00209654 |
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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 | 4000108876 |
ISBN | 9783540392491 |
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※2017年9月4日以降