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2010 Torsion in finite $H$-spaces and the homotopy of the three-sphere
Piotr Beben, Stephen Theriault
Homology Homotopy Appl. 12(2): 25-37 (2010).


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.


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Piotr Beben. Stephen Theriault. "Torsion in finite $H$-spaces and the homotopy of the three-sphere." Homology Homotopy Appl. 12 (2) 25 - 37, 2010.


Published: 2010
First available in Project Euclid: 28 January 2011

zbMATH: 1200.55013
MathSciNet: MR2721030

Primary: 55P45 , 55Q52

Keywords: Harper’s space , H-space , three sphere , torsion Lie group

Rights: Copyright © 2010 International Press of Boston

Vol.12 • No. 2 • 2010
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