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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Postnikov sections of formal and hyperformal spaces


Author: Samuel B. Smith
Journal: Proc. Amer. Math. Soc. 122 (1994), 893-903
MSC: Primary 55P62; Secondary 55S45
MathSciNet review: 1204385
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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

DOI: http://dx.doi.org/10.1090/S0002-9939-1994-1204385-5
PII: S 0002-9939(1994)1204385-5
Keywords: Rational homotopy theory, formality, hyperformality, minimal model
Article copyright: © Copyright 1994 American Mathematical Society