Homotopy and Homology Theory with Some Applications

Abstract

The purpose of this project is to study topological spaces in terms of certain groups as~ sociated with them, these groups are topological invariants in the sense that isomorphic groups are associated with hornomeomorphic spaces. We discuss two types of groups. The homotopy group for the lower~dimension spaces and homology groups for higher-dimension spaces. As an application of this study we present some computation of homotopy and homology group and prove several theorems in algebra and analysis.