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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles 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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Postnikov sections of formal and hyperformal spaces
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by Samuel B. Smith PDF
Proc. Amer. Math. Soc. 122 (1994), 893-903 Request permission

Abstract:

Let X be a simply connected CW complex and ${X_n}$ its nth Postnikov section. We prove that X is formal provided ${H^q}({X_n},\mathbb {Q})$ is additively generated by decomposables for all q and n with $q > n$. Recall from [4] that a space X is said to be hyperformal if its rational cohomology algebra is the quotient of a free graded algebra by an ideal generated by a regular sequence. Using the main result of Felix and Halperin’s paper (Trans. Amer. Math. Soc. 270 (1982), 575-588) we show our sufficient condition for formality is actually equivalent to hyperformality.
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Additional Information
  • © Copyright 1994 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 122 (1994), 893-903
  • MSC: Primary 55P62; Secondary 55S45
  • DOI: https://doi.org/10.1090/S0002-9939-1994-1204385-5
  • MathSciNet review: 1204385