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.References
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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