Torsion in finite H-spaces and the homotopy of the three-sphere

Let X be a 2-connected p-local finite H-space with a single cell in dimension three. We give a simple cohomological criterion which distinguishes when the inclusion i: S^3 \underset {\longrightarrow}{i} X has the property that the loop of its three-connected cover is null homotopic. In particular, s...

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Bibliographic Details
Published inHomology, homotopy, and applications Vol. 12; no. 2; pp. 25 - 37
Main Authors Beben, Piotr, Theriault, Stephen
Format Journal Article
LanguageEnglish
Published International Press of Boston 2010
Subjects
55P45
55Q52
H-space
Harper’s space
three sphere
torsion Lie group
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Summary:Let X be a 2-connected p-local finite H-space with a single cell in dimension three. We give a simple cohomological criterion which distinguishes when the inclusion i: S^3 \underset {\longrightarrow}{i} X has the property that the loop of its three-connected cover is null homotopic. In particular, such a null homotopy implies that \pi_m(i )= 0 for m \geq 4. Applications are made to Harper's rank 2 finite H-space and simple, simply-connected, compact Lie groups.
ISSN:1532-0073
1532-0081
DOI:10.4310/HHA.2010.v12.n2.a2