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Characterization and Topological Rigidity of Nöbeling Manifolds
Andrzej Nagórko, University of Warsaw, Poland

Memoirs of the American Mathematical Society
2013; 92 pp; softcover
Volume: 223
ISBN-10: 0-8218-5366-X
ISBN-13: 978-0-8218-5366-5
List Price: US$69
Individual Members: US$41.40
Institutional Members: US$55.20
Order Code: MEMO/223/1048
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The author develops a theory of Nöbeling manifolds similar to the theory of Hilbert space manifolds. He shows that it reflects the theory of Menger manifolds developed by M. Bestvina and is its counterpart in the realm of complete spaces. In particular the author proves the Nöbeling manifold characterization conjecture.

Table of Contents

Introduction and preliminaries
  • Introduction
  • Preliminaries
Reducing the proof of the main results to the construction of \(n\)-regular and \(n\)-semiregular \(\mathcal{N}_n\)-covers
  • Approximation within an \(\mathcal{N}_n\)-cover
  • Constructing closed \(\mathcal{N}_{n}\)-covers
  • Carrier and nerve theorems
  • Anticanonical maps and semiregularity
  • Extending homeomorphisms by the use of a "brick partitionings" technique
  • Proof of the main results
Constructing \(n\)-semiregular and \(n\)-regular \(\mathcal{N}_n\)-covers
  • Basic constructions in \(\mathcal{N}_{n}\)-spaces
  • Core of a cover
  • Proof of Theorem 6.7
  • Bibliography
  • Index
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