Geometric topology of generalized 3-manifolds |
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Authors: | Alberto Cavicchioli Dušan Repovš Thomas L. Thickstun |
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Affiliation: | (1) Dipartimento di Matematica, Università di Modena e Reggio Emilia, Via Campi 213/B, 41100 Modena, Italy;(2) Institute of Mathematics, Physics and Mechanics, University of Ljubljana, P.O. Box 2964, Ljubljana, 1001, Slovenia;(3) Department of Mathematics, Southwest Texas State University, San Marcos, TX 78666, USA |
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Abstract: | In this paper, we describe the history and the present status of one of the main classical problems in low-dimensional geometric topology—the recognition of topological 3-manifolds in the class of all generalized 3-manifolds (i.e., ANR homology 3-manifolds). This problem naturally splits into the cell-like resolution problem for 3-manifolds by means of homology 3-manifolds and the general-position problem for topological 3-manifolds. We have also included some open problems. __________ Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 11, No. 4, pp. 71–84, 2005. |
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