A new 3-dimensional shrinking criterion

Daverman, Robert J.; Repovš, Dušan

doi:10.1090/S0002-9947-1989-0978381-X

A new $3$-dimensional shrinking criterion
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by Robert J. Daverman and Dušan Repovš

Trans. Amer. Math. Soc. 315 (1989), 219-230

DOI: https://doi.org/10.1090/S0002-9947-1989-0978381-X

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Abstract:

We introduce a new shrinking criterion for cell-like upper semicontinuous decompositions $G$ of topological $3$-manifolds, such that the embedding dimension (in the sense of Štan’ko) of the nondegeneracy set of $G$ is at most one. As an immediate application, we prove a recognition theorem for $3$-manifolds based on a new disjoint disks property.

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