JournalsprimsVol. 29 , No. 3DOI 10.2977/prims/1195167049

Phantom Maps and Monoids of Endomorphisms of <i>K</i>(<b><i>Z</i></b>,<i>m</i>) x <i>S<sup>n</sup></i>

  • Yoshimi Shitanda

    Kyushu University, Fukuoka, Japan
Phantom Maps and Monoids of Endomorphisms of <i>K</i>(<b><i>Z</i></b>,<i>m</i>) x <i>S<sup>n</sup></i> cover

Abstract

The compositions hf, hg of phantom pair f, g and a phantom map h are homotopic. The compositions hf, kf of phantom pair h, k and a phantom map f are homotopic. We determine the homotopy set [K(Z,m) x Sn, K(Z,m) x Sn] and its monoid structure given by the composition of maps for all m, n ≥ 1.