Homotopy groups of the spaces of self-maps of Lie groups. II (Q1047770)

For connected based spaces \(X\) and \(Y\) let \(\text{map}_*(X,Y)\) denote the space consisting of all base point preserving maps \(f:X\to Y\). If \(X=Y=G\) is a Lie group, this becomes an \(H\)-space and it is interesting to determine the homotopy groups \(\pi_n(\text{map}_*(G,G))\). In this paper the authors study this problem for \(G=SU(3)\) or \(Sp(2)\). In this case, the homotopy group \(\pi_n(\text{map}_*(G,G))\) was already determined for \(0\leq n \leq 8\) by \textit{K. I. Mayurama} and \textit{H. Oshima} [J. Math. Soc. Japan 60, No.~3, 767--792 (2008; Zbl 1148.55002)] and and \textit{H. Mimura} and \textit{H. Oshima} [J. Math. Soc. Japan 51, No.~1, 71--92 (1999; Zbl 0931.55005)]. As a continuation of this work, in the present paper the authors compute it for \(9\leq n\leq 11\). The computation is based on the classical one which uses Toda brackets and cofiber sequences.