Binary Operations for Homotopy Groups with Coefficients

TL;DR

This paper introduces and analyzes binary operations on homotopy groups with coefficients, establishing their properties and relationships to classical products, and explores their applications to Moore spaces.

Contribution

It defines new binary operations, including Ext operations, and compares them to existing Whitehead and Torsion products, extending the understanding of homotopy group structures.

Findings

Binary operations can be homomorphic images of the generalized Whitehead product.

Introduces Ext operations and explores their properties.

Proves the smash product of Moore spaces has a specific homotopy type.

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.