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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles 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 1.48 .

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A stable converse to the Vietoris-Smale theorem with applications to shape theory
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by Steve Ferry PDF
Trans. Amer. Math. Soc. 261 (1980), 369-386 Request permission

Abstract:

Our main result says that if $f: X \to Y$ is a map between finite polyhedra which has k-connected homotopy fiber, then there is an n such that $f \times {\text {id:}} X \times {I^n} \to Y$ is homotopic to a map with k-connected point-inverses. This result is applied to give an algebraic characterization of compacta shape equivalent to locally n-connected compacta. We also show that a $U{V^1}$ compactum can be “improved” within its shape class until its homotopy theory and strong shape theory are the same with respect to finite dimensional polyhedra.
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Additional Information
  • © Copyright 1980 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 261 (1980), 369-386
  • MSC: Primary 55R65; Secondary 54C56, 55P55, 57N20, 57Q05, 57Q10
  • DOI: https://doi.org/10.1090/S0002-9947-1980-0580894-1
  • MathSciNet review: 580894