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

DOI:
https://doi.org/10.1090/S0002-9939-1994-1204385-5

MathSciNet review:
1204385

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Abstract: Let *X* be a simply connected CW complex and its *n*th Postnikov section. We prove that *X* is formal provided is additively generated by decomposables for all *q* and *n* with . 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:
https://doi.org/10.1090/S0002-9939-1994-1204385-5

Keywords:
Rational homotopy theory,
formality,
hyperformality,
minimal model

Article copyright:
© Copyright 1994
American Mathematical Society