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The First Turkish International Conference on Topology and its Applications
August 2-5, 2000
Istanbul University
Istanbul, Turkey

Organizers
Nurettin Ergun, Mahir Hasanov, Turgut Önder, Cem Tezer, Murat Tuncali, Stephen Watson

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Geometric topology of low-dimensional generalized manifolds
by
Dušan Repovš
University of Ljubljana

In this survey lecture we shall present recent work on the geometric aspects of topology of low dimensional generalized manifolds, i.e. 3- and 4-dimensional ANR homology manifolds. In particular, we shall study the main two problems - the resolution problem and the general position problem and will list related results due to Bestvina-Daverman-Venema-Walsh, Brahm, Cavicchioli-Repovs, Daverman-Repovs, Thickstun, and others. We shall compare these developments with well-known advances in higher dimensions due to Bryant-Ferry-Mio-Weinberger and will state several open problems and conjectures.

Date received: February 1, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caeh-02.