Cell-like 0-dimensional decompositions of 𝑆³ are 4-manifold factors

Daverman, R. J.; Row, W. H.

doi:10.1090/S0002-9947-1979-0539916-8

Cell-like $0$-dimensional decompositions of $S^{3}$ are $4$-manifold factors
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by R. J. Daverman and W. H. Row PDF

Trans. Amer. Math. Soc. 254 (1979), 217-236 Request permission

Abstract:

The main result is the title theorem asserting that if G is any upper semicontinuous decomposition of ${S^3}$ into cell-like sets which is 0-dimensional, in the sense that the image of the nondegenerate elements in ${S^3}/G$ is 0-dimensional, then $G \times {S^1}$ is shrinkable, and $\left ( {{S^3}/G} \right ) \times {S^1}$ is homeomorphic to ${S^3} \times {S^1}$.

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Suspensions of homology spheres

Approximating certain cell-like maps by homeomorphisms

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Cell-like

dimensional decompositions of