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International Conference on Topology and its Applications
August 23-27, 1999
Kanagawa University
Yokohama, Japan

Organizers
Yukinobu Yajima, the chairman, Masami Sakai, the vice-chairman, Yoshihiro Abe, Kazuhiro Sakai, Toshiji Terada, Kenichi Tamano, Akio Kato, Takao Hoshina, Hisao Kato, Kazuhiro Kawamura, Akira Koyama, Tsugunori Nogura

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Topology of generalized 3-manifolds: A survey
by
Dušan Repovš
University of Ljubljana, Slovenia

We shall present a short historical survey of the topology of generalized 3-manifolds, i.e. ENR homology 3-manifolds, from their early beginnings in 1930's to the present day. We shall concentrate on properties of these spaces which are particular for dimension 3 (in comparison with generalized (n>3)-manifolds, for the large part due to the unresolved status of the Poincare Conjecture. In the second part we shall present the current state of affairs on the two main problems concerning this class of spaces - the Resolution problem (the work of Bryant-Lacher, Brin-McMillan, Lacher-Repovs, Thickstun, and others) and the General position problem (the work of Bing, Lambert-Sher, Daverman-Eaton, Lacher-Repovs, Daverman-Repovs, Brahm, and others).

We shall list some open problems and related conjectures.

Date received: June 19, 1999

Copyright © 1999 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 # caby-14.