Algebraic Topology

TL;DR

This chapter introduces fundamental concepts of Algebraic Topology, emphasizing applications in physical sciences and including a review of computational methods like persistent homology.

Contribution

It offers an accessible overview of algebraic topology with a focus on practical applications and computational techniques.

Findings

Introduction to key algebraic topology concepts

Discussion of applications in physical sciences

Overview of computational methods like persistent homology

Abstract

The chapter provides an introduction to the basic concepts of Algebraic Topology with an emphasis on motivation from applications in the physical sciences. It finishes with a brief review of computational work in algebraic topology, including persistent homology.