English translation in Journal of Mathematical Sciences 144 (5) (2007), 4413-4422We 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 (that is, 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.
Geometric topology of generalized 3-manifolds / Cavicchioli, Alberto; Repovs, D; Thickstun, T. L.. - In: FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA. - ISSN 1560-5159. - STAMPA. - 11 (4):(2005), pp. 71-84. [10.1007/s10958-007-0279-y]
Geometric topology of generalized 3-manifolds
CAVICCHIOLI, Alberto;
2005
Abstract
English translation in Journal of Mathematical Sciences 144 (5) (2007), 4413-4422We 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 (that is, 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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