Homotopy-commutative -spaces

Authors:
James P. Lin and Frank Williams

Journal:
Proc. Amer. Math. Soc. **113** (1991), 857-865

MSC:
Primary 55P45; Secondary 55S05, 55S45

DOI:
https://doi.org/10.1090/S0002-9939-1991-1047005-2

MathSciNet review:
1047005

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Abstract: Let be an -space with , where and . In this article we prove that cannot be homotopy-commutative. Combining this result with a theorem of Michael Slack results in the following theorem: *Let* *be a homotopy-commutative* *-space with* *cohomology finitely generated as an algebra. Then* *is isomorphic as an algebra over* *to the* *cohomology of a torus producted with a finite number of* s *and* s.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1991-1047005-2

Keywords:
Homotopy-commutative -space,
cohomology operation,
Steenrod algebra

Article copyright:
© Copyright 1991
American Mathematical Society