Binary Operations for Homotopy Groups with Coefficients

Abstract

We define and study binary operations for homotopy groups with coefficients. We give conditions to prove that certain binary operations are the homomorphic image of the generalized Whitehead product. This allows carrying over properties of the generalized Whitehead product to these operations. We discuss two classes of binary operations, the Whitehead products and the Torsion products. We introduce a new class of operations called Ext operations and determine some of its properties. We compare the Torsion product to the Whitehead product in a special case. We prove that the smash product of two Moore spaces has the homotopy type of a wedge of two Moore spaces.