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Proceedings of the American Mathematical Society

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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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Keywords: Rational homotopy theory, formality, hyperformality, minimal model
Article copyright: © Copyright 1994 American Mathematical Society

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