Holomorphic curves in loop groups (Q1118051)

Let G be a compact simple Lie group. The paper is devoted to the study of the space \(Hol^*_ d(S^ 2,\Omega_{alg}G)\) of holomorphic basepoint preserving degree d maps f: \(S^ 2\to \Omega G\) of the 2-sphere \(S^ 2\) into the loop space \(\Omega\) G of G which satisfy the additional property that their image lies entirely in the subgroup of algebraic maps. The cell decomposition of \(Hol^*_ d(S^ 2,\Omega_{alg}G)\) is described. The Hausdorff dimension of \(Hol^*_ d(S^ 2,\Omega_{alg}SU_ n)\) is computed to be 2(2n-1)d.