Juno Mukai

Gottlieb and Whitehead Center Groups of Spheres, Projective and Moore Spaces

Introduction.- Gottlieb groups of Spheres.- Gottlieb and Whitehead Center Groups of Projective Spaces.- Gottlieb and Whitehead Center Groups of Moore Spaces.

Determination of the order of the P-image by Toda brackets

The present paper gives a proof of the authors paper in the Proceeding of the International Conference on Homotopy Theory and Related Topics at Korea University (2005), 109--113, on the orders of Whitehead products of iota_n with alpha in pi^n_{n+k}, (n > k+1, k < 25) and improves and extends it. The method is to use composition methods in the homotopy groups of spheres and rotation groups.

Gottlieb and Whitehead Center Groups of Projective Spaces

By the use of Siegel’s method and the classical results of homotopy groups of spheres and Lie groups, we determine in this chapter some Gottlieb groups of projective spaces or give the lower bounds of their orders. Furthermore, making use of the properties of Whitehead products, we determine some Whitehead center groups of projective spaces.

Gottlieb and Whitehead Center Groups of Moore Spaces

This chapter takes up the systematic study of the Gottlieb groups \(G_{n+k}(M(A,n))\) of Moore spaces M(A, n) for an abelian group A and n ≥ 2. The groups \(G_{n+k}(M(A,n))\) and \(G_{n+k}(M(A \oplus \mathbb{Z},n))\) are determined for k = 0, 1, 2, 3, 4, 5 and n ≥ 2 provided A is finite.