Homology, Homotopy and Applications

Volume 12 (2010)

Number 2

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

Pages: 25 – 37

DOI: https://dx.doi.org/10.4310/HHA.2010.v12.n2.a2


Piotr Beben (University of Northern British Columbia, Prince George, B.C., Canada)

Stephen Theriault (Department of Mathematical Sciences, University of Aberdeen, Scotland, United Kingdom)


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 $i$: $S^3 →X$ has the property that the loop of its three-connected cover is null homotopic. In particular, such a null homotopy implies that $π_m(i)=0 for m ≥4$. Applications are made to Harper’s rank 2 finite $H$-space and simple, simply-connected, compact Lie groups.


$H$-space; Harper’s space; torsion Lie group; three sphere

2010 Mathematics Subject Classification

55P45, 55Q52

Published 1 January 2010