The 23-rd and 24-th homotopy groups of the n-th rotation group

Abstract

We denote by π k (R n ) the k-th homotopy group of the n-th rotation group R n and π k (R n : 2) the 2-primary components of it. We determine the group structures of π k (R n : 2) for k = 23 and 24 by use of the fibration R n+1 Rn −→S n . The method is based on Toda's composition methods.