A book on Algebraic Topology

[Marco Grandis <grandis@dima.unige.it>]

This new book is an introduction to Algebraic Topology, structurally based on Homological Algebra and Category Theory:
 
Marco Grandis
Algebraic Topology, A Structural Introduction
World Scientific Publishing Company, 2022, x + 362 pages

https://www.worldscientific.com/worldscibooks/10.1142/12586

Downloadable Introduction:
https://www.worldscientific.com/doi/epdf/10.1142/9789811248368_0001


Presentation

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:
 	•	Preface
 	•	Introduction
 	•	Introducing Algebraic Topology
 	•	Singular Homology
 	•	Relative Singular Homology and Homology Theories
 	•	Singular Homology with Coefficients
 	•	Derived Functors, Universal Coefficients and Products
 	•	An Introduction to Homotopy Groups
 	•	Complements on Categories and Topology
 	•	Solutions to the Exercises
 	•	References
 	•	Index


Marco Grandis

e-mail: grandis@dima.unige.it
http://www.dima.unige.it/~grandis/



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