FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2005, VOLUME 11, NUMBER 4, PAGES 71-84

Geometric topology of generalized 3-manifolds

A. Cavicchioli
D. Repovš
T. L. Thickstun

Abstract

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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.

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