Boundedly controlled topology : foundations of algebraic topology and simple homotopy theory / Douglas R. Anderson, Hans J. Munkholm.

By: Anderson, Douglas R. (Douglas Ross), 1940-
Contributor(s): Munkholm, Hans J. (Hans Jørgen), 1940-
Material type: TextTextSeries: Lecture notes in mathematics (Springer-Verlag): 1323.Publisher: Berlin ; New York : Springer-Verlag, ©1988Description: 1 online resource (xii, 309 pages)Content type: text Media type: computer Carrier type: online resourceISBN: 9783540392491; 3540392491Subject(s): Piecewise linear topology | Homotopy theory | Complexes | Categories (Mathematics) | Complexes (Mathématiques) | Catégories (Mathématiques) | Categories (Mathematics) | Complexes | Homotopy theory | Piecewise linear topology | Algebraische Topologie | Einfache Homotopietheorie | KategorientheorieGenre/Form: Electronic books. Additional physical formats: Print version:: Boundedly controlled topology.DDC classification: 510 s | 514/.22 LOC classification: QA3 | .L28 no. 1323 | QA613.4Other classification: 31.65 Online resources: Click here to access online
Contents:
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 -- Bibliography -- Index.
Action note: digitized 2011 committed to preserveSummary: 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.
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Includes bibliographical references (pages 301-304) and index.

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 -- Bibliography -- Index.

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.

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