Cohomotopy sets of projective planes

摘要

We set F = R (real), C (complex), H (quaternion), O (octonian) and d=dim_R F. We denote by FP~2 the F-projective plane. The purpose of this note is to determine the cohomotopy set π~n(FP~2) = [FP~2, S~n]. Let h = h(F): S~(2d-1) → S~d be the Hopf map.