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An exotic factor of S3 × ℝ

Published online by Cambridge University Press:  24 October 2008

W. Jakobsche  and
D. Repovš
W. Jakobsche
Affiliation:
University of Warsaw, 00-901 Warsaw, Poland
D. Repovš
Affiliation:
University of Ljubljana, 61000 Ljubljana, Yugoslavia
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Extract

Cannon's recognition problem [10] asks for a short list of topological properties that is reasonably easy to check and that characterizes topological manifolds. In dimensions below three the answer has been known for a long time: see [6, 24]. In dimensions above four it is now known, due to the work of J. W. Cannon [11], R. D. Edwards [14] (see also [12] and [18]), and F. S. Quinn [21], that topological n-manifolds (n ≥ 5) are precisely ENR ℤ-homology n-manifolds with Cannon's disjoint disc property (DDP) [11] and with a vanishing Quinn's local surgery obstruction [23]. In dimension four there is a resolution theorem of Quinn [22] (with the same obstruction as in dimensions ≥ 5) and a 1-LCC shrinking theorem of M. Bestvina and J. J. Walsh [5]. However, it is still an open problem to find an effective analogue of Cannon's DDP for this dimension, one which would yield a shrinking theorem along the lines of that of Edwards [14]. For more on the history of the recognition problem see the survey [24].

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 107 , Issue 2 , March 1990 , pp. 329 - 344
Copyright
Copyright © Cambridge Philosophical Society 1990

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References

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