CBMS Regional Conference Series in Mathematics 1976; 131 pp; softcover Number: 28 Reprint/Revision History: reprinted 1982 ISBN10: 0821816780 ISBN13: 9780821816783 List Price: US$25 Member Price: US$20 All Individuals: US$20 Order Code: CBMS/28
 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 Reviews "This is an important contribution, since it compiles known results from a variety of papers into one wellwritten source."  Mathematical Reviews Table of Contents  Preliminaries
 Zsets in Q
 Stability of Qmanifoldsitle>
 Zsets in Qmanifolds
 Qmanifolds of the form \(M \times [0, 1)\)
 Shapes of Zsets in Q
 Near homeomorphisms and the Sum Theorem
 Applications of the Sum Theorem
 The Splitting Theorem
 The Handle Straightening Theorem
 The Triangulation Theorem
 The Classification Theorem
 Celllike mappings
 The ANR Theorem
 References
 Appendix Open problems in infinitedimensional topology
