From H8401689@SUBMATHS.hku.hk Fri Jan 23 04:46:04 1998
Date: Fri, 23 Jan 1998 17:50:38 GMT+8
I am a postgraduate student of University of Hong Kong. Now I tackle
a problem concerning the solvability of a quaternionic equation. I
can complete my proof if I can show that a function
$f:S^3\to\text{GL}(n,\mathbb{H})$, defined by $f(q)=q^m I_n$, is not
homotopic to a constant mapping. I conjecture that
$\pi_3(\text{GL}(n,\mathbb{H}))$ is isomorphic to $\mathbb{Z}$ and
$f$ corresponds to the integer $mn$. Is is true? Actually I am a
layman of algebraic topology. So, I cannot work out rigorous proofs
by myself. Would you give me some advice or reference to settle my
problem? Thank you very much.
Regards, Lok-Shun Siu.