A new 3-dimensional shrinking criterion

Abstract

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