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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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A new $3$-dimensional shrinking criterion
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by Robert J. Daverman and Dušan Repovš PDF
Trans. Amer. Math. Soc. 315 (1989), 219-230 Request permission

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
  • © Copyright 1989 American Mathematical Society
  • 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