Resolutions of generalized 3-manifolds whose singular sets have general position dimension one,☆☆

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Abstract

We show that, modulo the classical Poincaré Conjecture, a closed generalized 3-manifold X is the cell-like image of a closed 3-manifold (i.e., is “resolvable”) if it satisfies the following condition: any map of a disk into X can be approximated by one whose image meets the singular set of X in a zero-dimensional set.

MSC

57P99
57M35
57N10

Keywords

Generalized 3-manifold
Resolution
Cell-like
Loop theorem

Cited by (0)

Research supported in part by an SWTSU developmental leave.

☆☆

An earlier preprint version of this paper was entitled, “A further extension of the Loop Theorem and resolutions of generalized 3-manifolds with 1-demensional singular set”.