Advances in Algebraic Topology: A Survey of Recent Developments

Abstract

This survey paper presents an overview of recent advances in algebraic topology, highlighting key developments in homotopy theory, homology groups, cohomology theory, and their applications in understanding the structure of topological spaces. We discuss the fundamental concepts of simplicial complexes and their role in providing a combinatorial framework for studying topological spaces. The paper emphasizes the interplay between algebraic and geometric methods in addressing contemporary challenges in algebraic topology, with a focus on current research trends and open problems