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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

A new $ 3$-dimensional shrinking criterion


Authors: Robert J. Daverman and Dušan Repovš
Journal: Trans. Amer. Math. Soc. 315 (1989), 219-230
MSC: Primary 57N60; Secondary 57M40, 57P05
DOI: https://doi.org/10.1090/S0002-9947-1989-0978381-X
MathSciNet review: 978381
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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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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1989-0978381-X
Keywords: Cell-like map, shrinking criterion, embedding dimension, recognition theorem, resolution disjoint disks property, light map separation property
Article copyright: © Copyright 1989 American Mathematical Society