Characterization and Topological Rigidity of Nöbeling Manifolds.

Intro -- Contents -- Abstract -- Part 1 . Introduction and preliminaries -- Chapter 1. Introduction -- Chapter 2. Preliminaries -- 2.1. Covers and interior covers -- 2.2. Absolute extensors -- 2.3. Nerves of covers and barycentric stars -- 2.4. Strong universality -- 2.5. -Homotopy equivalence -- 2.6. -sets -- Part 2 . Reducing the proof of the main results to the construction of -regular and -semiregular \ { }-covers -- Chapter 3. Approximation within an _{ }-cover -- 3.1. (ℱ)-sets -- 3.2. Approximation within a cover -- 3.3. -collections\footnote{we shall not use the theorem proved in ths section until the third part of the paper.} -- Chapter 4. Constructing closed _{ }-covers -- 4.1. Adjustment of a collection -- 4.2. Limits of sequences of adjustments -- 4.3. Construction of a closed _{ }-swelling -- Chapter 5. Carrier and nerve theorems -- 5.1. Regular covers -- 5.2. Carrier theorem -- 5.3. Nerve theorem -- Chapter 6. Anticanonical maps and semiregularity -- 6.1. A nerve theorem and the notion of semiregularity -- 6.2. A construction of regular covers -- 6.3. A construction of semiregular covers -- Chapter 7. Extending homeomorphisms by the use of a "brick partitionings" technique -- Chapter 8. Proof of the main results -- Part 3 . Constructing -semiregular and -regular \ { }-covers -- Chapter 9. Basic constructions in _{ }-spaces -- 9.1. Adjustment to a -collection -- 9.2. Fitting closed _{ }-neighborhoods -- 9.3. Patching of holes -- Chapter 10. Core of a cover -- 10.1. The existence of an -core -- 10.2. An -core of a limit of a sequence of deformations -- 10.3. Proof of theorem 10.1 -- 10.4. Retraction onto a core and a proof of theorem 6.17 -- Chapter 11. Proof of theorem 6.7 -- 11.1. Patching of small holes -- 11.2. ⊚-Contractibility -- 11.3. Proof of theorem 6.7 for =0.

11.4. ⋓-Contractibility -- 11.5. Patching of large holes -- 11.6. Proof of theorem 6.7 for &gt -- 0 -- Bibliography -- Index.

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