A. Cavicchioli, D. Repovš, T. Thickstun, “Geometric topology of generalized <nobr>$3$</nobr>-manifolds”, Fundam. Prikl. Mat., 2005, Volume 11, Issue 4,Pages <nobr>71

This article is cited in 4 papers

Geometric topology of generalized $3$-manifolds

A. Cavicchioli^a, D. Repovš^b, T. Thickstun^c

^a University of Modena and Reggio Emilia
^b University of Ljubljana
^c Texas State University-San Marcos

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.

UDC: 515.162.3+515.163