Electronic ISBN:  9781470423889 
Product Code:  CBMS/28.E 
List Price:  $25.00 
Individual Price:  $20.00 

Book DetailsCBMS Regional Conference Series in MathematicsVolume: 28; 1976; 131 ppMSC: Primary 57;
The goal of these lectures is to present an introduction to the geometric topology of the Hilbert cube Q and separable metric manifolds modeled on Q, which are called here Hilbert cube manifolds or Qmanifolds. In the past ten years there has been a great deal of research on Q and Qmanifolds which is scattered throughout several papers in the literature. The author presents here a selfcontained treatment of only a few of these results in the hope that it will stimulate further interest in this area. No new material is presented here and no attempt has been made to be complete. For example, the author has omitted the important theorem of SchoriWest stating that the hyperspace of closed subsets of \([0,1]\) is homeomorphic to Q. In an appendix (prepared independently by R. D. Anderson, D. W. Curtis, R. Schori and G. Kozlowski) there is a list of problems which are of current interest. This includes problems on Qmanifolds as well as manifolds modeled on various linear spaces. The reader is referred to this for a much broader perspective of the field.
In the first four chapters, the basic tools which are needed in all of the remaining chapters are presented. Beyond this there seem to be at least two possible courses of action. The reader who is interested only in the triangulation and classification of Qmanifolds should read straight through (avoiding only Chapter VI). In particular the topological invariance of Whitehead torsion appears in Section 38. The reader who is interested in R. D. Edwards' recent proof that every ANR is a Qmanifold factor should read the first four chapters and then (with the single exception of 26.1) skip over to Chapters XIII and XIV.Readership 
Table of Contents

Chapters

I. Preliminaries

II. ZSets in Q

III. Stability of QManifofds

IV. ZSets in QManifolds

V. QManifolds of the Form M x [0,1)

VI. Shapes of ZSets in Q

VII. Near Homeomorphisms and the Sum Theorem

VIII. Applications of the Sum Theorem

IX. The Splitting Theorem

X. The Handle Straightening Theorem

XI. The Triangulation Theorem

XII. The Classification Theorem

XIII. CellLike Mappings

XIV. The ANR Theorem


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This is an important contribution, since it compiles known results from a variety of papers into one wellwritten source.
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The goal of these lectures is to present an introduction to the geometric topology of the Hilbert cube Q and separable metric manifolds modeled on Q, which are called here Hilbert cube manifolds or Qmanifolds. In the past ten years there has been a great deal of research on Q and Qmanifolds which is scattered throughout several papers in the literature. The author presents here a selfcontained treatment of only a few of these results in the hope that it will stimulate further interest in this area. No new material is presented here and no attempt has been made to be complete. For example, the author has omitted the important theorem of SchoriWest stating that the hyperspace of closed subsets of \([0,1]\) is homeomorphic to Q. In an appendix (prepared independently by R. D. Anderson, D. W. Curtis, R. Schori and G. Kozlowski) there is a list of problems which are of current interest. This includes problems on Qmanifolds as well as manifolds modeled on various linear spaces. The reader is referred to this for a much broader perspective of the field.
In the first four chapters, the basic tools which are needed in all of the remaining chapters are presented. Beyond this there seem to be at least two possible courses of action. The reader who is interested only in the triangulation and classification of Qmanifolds should read straight through (avoiding only Chapter VI). In particular the topological invariance of Whitehead torsion appears in Section 38. The reader who is interested in R. D. Edwards' recent proof that every ANR is a Qmanifold factor should read the first four chapters and then (with the single exception of 26.1) skip over to Chapters XIII and XIV.

Chapters

I. Preliminaries

II. ZSets in Q

III. Stability of QManifofds

IV. ZSets in QManifolds

V. QManifolds of the Form M x [0,1)

VI. Shapes of ZSets in Q

VII. Near Homeomorphisms and the Sum Theorem

VIII. Applications of the Sum Theorem

IX. The Splitting Theorem

X. The Handle Straightening Theorem

XI. The Triangulation Theorem

XII. The Classification Theorem

XIII. CellLike Mappings

XIV. The ANR Theorem

This is an important contribution, since it compiles known results from a variety of papers into one wellwritten source.
Mathematical Reviews