M – Homotopy Functions and Their Equivalences in Algebraic Topology: A New Perspective

Abstract

This paper explores the complex realm of multivalued homotopy functions in algebraic topology. It covers four main areas: the foundational concepts of multivalued homotopy functions, the group operations within these functions, the action of the multivalued fundamental group on homotopy classes, and the criteria for the equivalence of multivalued homotopy functions. By examining these aspects, we reveal new algebraic structures, symmetries, and deeper connections between topological spaces and their algebraic invariants, providing a comprehensive framework for understanding and classifying multivalued homotopy functions.