Boundedly controlled topology : foundations of algebraic topology and simple homotopy theory /
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| Author / Creator: | Anderson, Douglas R. (Douglas Ross), 1940- |
|---|---|
| Imprint: | Berlin ; New York : Springer-Verlag, ©1988. |
| Description: | 1 online resource (xii, 309 pages). |
| Language: | English |
| Series: | Lecture notes in mathematics, 0075-8434 ; 1323 Lecture notes in mathematics (Springer-Verlag) ; 1323. |
| Subject: | |
| Format: | E-Resource Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/11069777 |
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| 100 | 1 | |a Anderson, Douglas R. |q (Douglas Ross), |d 1940- |0 http://id.loc.gov/authorities/names/n87906667 |1 http://viaf.org/viaf/47396827 | |
| 245 | 1 | 0 | |a Boundedly controlled topology : |b foundations of algebraic topology and simple homotopy theory / |c Douglas R. Anderson, Hans J. Munkholm. |
| 260 | |a Berlin ; |a New York : |b Springer-Verlag, |c ©1988. | ||
| 300 | |a 1 online resource (xii, 309 pages). | ||
| 336 | |a text |b txt |2 rdacontent |0 http://id.loc.gov/vocabulary/contentTypes/txt | ||
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| 490 | 1 | |a Lecture notes in mathematics, |x 0075-8434 ; |v 1323 | |
| 504 | |a Includes bibliographical references (pages 301-304) and index. | ||
| 505 | 0 | |a 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. | |
| 520 | |a 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. | ||
| 506 | |3 Use copy |f Restrictions unspecified |2 star |5 MiAaHDL | ||
| 533 | |a Electronic reproduction. |b [S.l.] : |c HathiTrust Digital Library, |d 2011. |5 MiAaHDL | ||
| 538 | |a Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002. |u http://purl.oclc.org/DLF/benchrepro0212 |5 MiAaHDL | ||
| 583 | 1 | |a digitized |c 2011 |h HathiTrust Digital Library |l committed to preserve |2 pda |5 MiAaHDL | |
| 588 | 0 | |a Print version record. | |
| 650 | 0 | |a Piecewise linear topology. |0 http://id.loc.gov/authorities/subjects/sh85102031 | |
| 650 | 0 | |a Homotopy theory. |0 http://id.loc.gov/authorities/subjects/sh85061803 | |
| 650 | 0 | |a Complexes. |0 http://id.loc.gov/authorities/subjects/sh85029372 | |
| 650 | 0 | |a Categories (Mathematics) |0 http://id.loc.gov/authorities/subjects/sh85020992 | |
| 650 | 6 | |a Complexes (Mathématiques) | |
| 650 | 6 | |a Catégories (Mathématiques) | |
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| 650 | 7 | |a Complexes. |2 fast |0 (OCoLC)fst00871597 | |
| 650 | 7 | |a Homotopy theory. |2 fast |0 (OCoLC)fst00959852 | |
| 650 | 7 | |a Piecewise linear topology. |2 fast |0 (OCoLC)fst01063865 | |
| 650 | 0 | 7 | |a Algebraische Topologie. |2 swd |
| 650 | 0 | 7 | |a Einfache Homotopietheorie. |2 swd |
| 650 | 0 | 7 | |a Kategorientheorie. |2 swd |
| 655 | 4 | |a Electronic books. | |
| 700 | 1 | |a Munkholm, Hans J. |q (Hans Jørgen), |d 1940- |0 http://id.loc.gov/authorities/names/n87906665 |1 http://viaf.org/viaf/62184484 | |
| 776 | 0 | 8 | |i Print version: |a Anderson, Douglas R. (Douglas Ross), 1940- |t Boundedly controlled topology. |d Berlin ; New York : Springer-Verlag, ©1988 |z 0387193979 |w (DLC) 88016054 |w (OCoLC)18052132 |
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