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Proceedings of the American Mathematical Society

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

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Shape aspherical compacta–applications of a theorem of Kan and Thurston to cohomological dimension and shape theories
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by Takahisa Miyata PDF
Proc. Amer. Math. Soc. 129 (2001), 2783-2788 Request permission

Abstract:

Dydak and Yokoi introduced the notion of shape aspherical compactum. In this paper, we use this notion to obtain a generalization of Kan and Thurston theorem for compacta and pro-homology. As an application, we obtain a characterization of cohomological dimension with coefficients in $\mathbb {Z}$ and $\mathbb {Z}/p$ ($p$ prime) in terms of acyclic maps from a shape aspherical compactum, which improves the theorems of Edwards and Dranishnikov. Furthermore, we obtain the shape version of the theorem and as a consequence we show that every compactum has the stable shape type of a shape aspherical compactum.
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Additional Information
  • Takahisa Miyata
  • Affiliation: Department of Computer Science, Shizuoka Institute of Science and Technology, 2200-2 Toyosawa, Fukuroi, Shizuoka-Pref., 437-8555 Japan
  • Email: miyata@mb.sist.ac.jp
  • Received by editor(s): August 16, 1999
  • Received by editor(s) in revised form: December 29, 1999
  • Published electronically: January 18, 2001
  • Communicated by: Ronald A. Fintushel
  • © Copyright 2001 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 129 (2001), 2783-2788
  • MSC (1991): Primary 55M10, 55P55; Secondary 54F45, 55N05
  • DOI: https://doi.org/10.1090/S0002-9939-01-05852-X
  • MathSciNet review: 1838803