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Tractable formulas for v_1-periodic homotopy groups of SU(n) if
n < p^2-p+2

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Donald M. Davis and Huajian Yang

Last updated Feb. 1995.
### Abstract

Let p be a fixed odd prime. In [Davis, Proc LMS 1991], it was proved that for
d=0 and 1,
v_1^{-1}\pi_{2k-d}(SU(n)) has order p^{e(k,n)},
where e(k,n)=\min\{\nu_p(j!S(k,j)):n\le j\le k\}, with S(k,j) the
Stirling number of the second kind. In this paper, we give a more tractable
formula for e(k,n) when n < p^2-p+2 by calculating the unstable
Novikov spectral sequence. We also determine the abelian group structure
when d=1; it was known to be cyclic when d=0.
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