TRACTABLE FORMULAS FOR v1-PERIODIC HOMOTOPY
GROUPS OF SU(n) WHEN n p2 p + 1
DONALD M. DAVIS AND HUAJIAN YANG
1. Statement of results
Let p be a fixed odd prime. The (p-local)v1-periodic homotopy groups, v11ss (* *X),
of a space X were defined in [8]. Roughly speaking,they tell the portion of the* * p-local
homotopy groups of X detected byK -theory. For a spherically resolved space X,
each group v11ssi(X) is a direct summand of some actual homotopy group ssL(X).
We will focus on the case where Xis one of the special unitary groups SU(n), wh* *ich
are spherically resolved by the fibrations
(1.1) S U(n 1) ! SU(n) ! S2n1: