User carl mctague - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-25T07:36:11Z http://mathoverflow.net/feeds/user/6552 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/1922/what-is-the-cayley-projective-plane/27050#27050 Answer by Carl McTague for What is the Cayley projective plane? Carl McTague 2010-06-04T14:52:53Z 2011-02-20T11:20:07Z <p>A quick note about the homotopy groups of the Cayley plane. Mimura computed some of them. Specifically for <em>i</em>=8,9,10,...,23 he computed that $\pi_i\mathbf{CaP}^2$ equals <strong>Z</strong>, <strong>Z</strong>/2, <strong>Z</strong>/2, <strong>Z</strong>/24, 0, 0, <strong>Z</strong>/2, <strong>Z</strong>/120, (<strong>Z</strong>/2)$^{\oplus3}$, (<strong>Z</strong>/2)$^{\oplus4}$, <strong>Z</strong>/24$\oplus$ <strong>Z</strong>/2, <strong>Z</strong>/504$\oplus$ <strong>Z</strong>/2, 0, <strong>Z</strong>/6, <strong>Z</strong>/4, <strong>Z</strong>$\oplus$ <strong>Z</strong>/120$\oplus$ (<strong>Z</strong>/2)$^{\oplus2}$, respectively. See Theorem 7.2 of his 1967 paper <em>The homotopy groups of Lie groups of low rank</em>:<br> &nbsp; <a href="http://www.ams.org/mathscinet-getitem?mr=206958" rel="nofollow">http://www.ams.org/mathscinet-getitem?mr=206958</a><br> &nbsp; <a href="http://projecteuclid.org/euclid.kjm/1250524375" rel="nofollow">http://projecteuclid.org/euclid.kjm/1250524375</a></p>