ALGEBRAIC TOPOLOGY: A STRUCTURAL INTRODUCTION

Algebraic Topology is a system and strategy of partial translations, aiming to reduce difficult topological problems to algebraic facts that can be more easily solved. The main subject of this book is singular homology, the simplest of these translations. Studying this theory and its applications, we also investigate its underlying structural layout - the topics of Homological Algebra, Homotopy Theory and Category Theory which occur in its foundation.

This book is an introduction to a complex domain, with references to its advanced parts and ramifications. It is written with a moderate amount of prerequisites — basic general topology and little else — and a moderate progression starting from a very elementary beginning. A consistent part of the exposition is organised in the form of exercises, with suitable hints and solutions.

It can be used as a textbook for a semester course or self-study, and a guidebook for further study.

Contents:

PrefaceIntroductionIntroducing Algebraic TopologySingular HomologyRelative Singular Homology and Homology TheoriesSingular Homology with CoefficientsDerived Functors, Universal Coefficients and ProductsAn Introduction to Homotopy GroupsComplements on Categories and TopologySolutions to the ExercisesReferencesIndex

Readership: Graduate students, PhD students and Researchers in Mathematics and Physics interested in Algebraic Topology.

'The author's approach to the subject is based very much on introducing the algebraic concepts before the topological ones. Presumably this is what the author means when he describes the book as a 'structured approach'. The exposition also relies on the use of many exercises and worked examples that are used to guide the reader through the development of the material.' - ZBMath Open