Algebraic Topology (Dover Books on Mathematics)

Book Details

• Publisher: Dover

• Author: C. R. F. Maunder

• Language: English

• ISBN: 9780486691312

• Pages: 400

• Cover: Paperback

• Edition: New edition

• Release Date: 14-06-1996

• Dimensions: 8.4 x 5.4 x 0.8 inches

About The Book

Elementary Algebraic Topology by C. R. F. Maunder is a thorough and modern treatment of elementary algebraic topology, ideal for advanced undergraduate and first-year graduate students. The book focuses on the homotopy-theoretic viewpoint of algebraic topology, making it a valuable resource for courses on homotopy and homology theory. It aims to translate topological problems into algebraic terms, a key goal of algebraic topology, to offer better solutions through the use of homology and homotopy groups.

The text covers important topics such as the construction of algebraic invariants, the classification of surfaces, and duality theorems for manifolds. Maunder also provides in-depth coverage of homotopy theory, CW-complexes, and co-homology groups associated with a general Ω-spectrum. These topics are explored with a strong focus on clarity, making the book suitable for both beginners and students ready to tackle more advanced topics in algebraic topology.

Key Topics Covered:

• Homotopy Theory: An exploration of the fundamental aspects of homotopy theory.

• CW-Complexes: A treatment of CW-complexes and their role in algebraic topology.

• Co-homology Groups: Detailed explanation of co-homology groups, particularly those associated with Ω-spectra.

• Duality in Homology Manifolds: The concept of duality in homology manifolds is thoroughly examined.

• Topological Problems and Solutions: How algebraic topology translates topological problems into algebraic ones for easier solutions.

• Classification of Surfaces: A comprehensive study on the classification of surfaces in topological spaces.

• Applications: Various applications of algebraic topology to real-world problems.

Features:

• Sophisticated and Modern Treatment: A deep dive into algebraic topology from a modern, homotopy-theoretic perspective.

• Detailed Examples and Exercises: Numerous examples and exercises are provided to aid comprehension and encourage active learning.

• Historical Development: Each chapter ends with notes and references that trace the historical development of the subject and guide the reader to more advanced results.

• Clear Writing Style: The author’s clear, detailed writing ensures students understand both the concepts and the reasoning behind them.

This book is an excellent resource for students studying algebraic topology, offering both theoretical depth and practical applications. It is particularly valuable for those interested in understanding the connection between algebra and topology through the lens of homotopy theory.