| I use the results of Bendersky and Thompson for the E(1)-based E2-term of S2 n+1, Es,t2KS2n+1 , and the results of Bendersky and Davis concerning the v 1-periodic groups of SU(n) to compute the E(1)-based E2-term for X = SU(n) for all primes p. This computation is performed using the Bendersky Thompson spectral sequence for SU(n). For spaces like SU(n) this spectral sequence converges to homotopy groups of the K-theory completion of SU( n), denoted pi* SU&d14; (n). Of particular interest is the existence of infinitely many divisible groups in the homotopy groups of the K-theory completion of SU which offers an example of how E-completion does not commute with direct limits. |
