Boundedly controlled topology : foundations of algebraic topology and simple homotopy theory /

Boundedly controlled topology : foundations of algebraic topology and simple homotopy theory /

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Bibliographic Details
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:	Piecewise linear topology. Homotopy theory. Complexes. Categories (Mathematics) Categories (Mathematics) Complexes. Homotopy theory. Piecewise linear topology.
Format:	E-Resource Book
URL for this record:	http://pi.lib.uchicago.edu/1001/cat/bib/11069777

Hidden Bibliographic Details
Other authors / contributors:	Munkholm, Hans J. (Hans Jørgen), 1940-
ISBN:	9783540392491 3540392491 0387193979 9780387193977
Notes:	Includes bibliographical references (pages 301-304) and index. Restrictions unspecified Electronic reproduction. [S.l.] : HathiTrust Digital Library, 2011. 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. http://purl.oclc.org/DLF/benchrepro0212 digitized 2011 HathiTrust Digital Library committed to preserve Print version record.
Summary:	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.
Other form:	Print version: Anderson, Douglas R. (Douglas Ross), 1940- Boundedly controlled topology. Berlin ; New York : Springer-Verlag, ©1988 0387193979

Table of 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.