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Zbl 0715.55010
Cohen, F.R.; Moore, J.C.; Neisendorfer, J.A.
Exponents in homotopy theory.
(English)
[A] Algebraic topology and algebraic K-theory, Proc. Conf., Princeton, NJ (USA), Ann. Math. Stud. 113, 3-34 (1987).

[For the entire collection see Zbl 0694.00022.] \par The main result states that if X is a simply connected space with only one nontrivial homology group $H\sb i(X;Z)$, and this satisfies $i\ge 3$ and $p\sp rH\sb i(X;Z)=0$ for some odd prime p, then $p\sp{2r+1}\pi\sb j(X)=0$ for all $j\ge 3$. The result is viewed as a small piece of evidence for a conjecture of Barratt which states that if p is a prime, and Y is a pointed space such that the order of the identity of $\Sigma\sp 2X$ is $p\sp n$, then the order of the identity of $\Omega\sp 2\Sigma\sp 2X$ is $p\sp{n+1}$. The proof of the main result utilizes various splitting results proved by the authors in Ann. Math., II. Ser. 109, 121-168 (1979; Zbl 0405.55018) and ibid. 110, 549-565 (1979; Zbl 0443.55009).
[D.Davis]
MSC 2000:
*55Q20 Homotopy groups of wedges, etc.

Keywords: homotopy groups; Moore spaces; exponents; simply connected space

Citations: Zbl 0694.00022; Zbl 0405.55018; Zbl 0443.55009

Cited in: Zbl 1148.55004

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Scientific prize winners of the ICM 2010
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Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

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