Boundedly Controlled Topology

1. Front Matter

   Pages I-XII

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2. Category theoretic foundations

   • Douglas R. Anderson, Hans J. Munkholm

   Pages 1-39

3. The algebraic topology of boundedly controlled spaces

   • Douglas R. Anderson, Hans J. Munkholm

   Pages 40-98

4. The geometric, boundedly controlled whitehead group

   • Douglas R. Anderson, Hans J. Munkholm

   Pages 99-122

5. Free and projective rpg modules the algebraic whitehead groups of rpg

   • Douglas R. Anderson, Hans J. Munkholm

   Pages 123-175

6. The isomorphism between the geometric and algebraic whitehead groups

   • Douglas R. Anderson, Hans J. Munkholm

   Pages 176-211

7. Boundedly controlled manifolds and the s-cobordism theorem

   • Douglas R. Anderson, Hans J. Munkholm

   Pages 212-259

8. Toward computations

   • Douglas R. Anderson, Hans J. Munkholm

   Pages 260-300

9. Back Matter

   Pages 301-309

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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.

• Algebraic topology
• Homotopy
• homotopy theory
• topology

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