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Jan 3, 2014 at 3:58 vote accept user44651
Jan 2, 2014 at 20:07 comment added Tyler Lawson These 2-torsion classes can be realized by maps from a mod-2 Moore spectrum such as $S^1 \to \Sigma M(2) \to S$, and the Moore spectrum has a map $\Sigma^8 M(2) \to M(2)$ which, upon precomposition, induces the 8-fold periodicity $KO_i(pt) \to KO_{i+8}(pt)$, so your proof actually implies surjectivity onto all the torsion classes of $KO$.
Jan 2, 2014 at 18:52 history edited ya-tayr CC BY-SA 3.0
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Jan 2, 2014 at 17:50 review First posts
Jan 2, 2014 at 18:07
Jan 2, 2014 at 17:32 history answered ya-tayr CC BY-SA 3.0