Algebraic Topology (Dover Books on Mathematics) by C. R. F. Maunder (PDF)

Description

Based on lectures to advanced undergraduate and first-year graduate students, this is a thorough, sophisticated and modern treatment of elementary algebraic topology, essentially from a homotopy theoretic viewpoint. The presentation of the homotopy theory and the account of duality in homology manifolds make the text ideal for a course on either homotopy or homology theory.The idea of algebraic topology is to translate problems in topology into problems in algebra with the hope that they have a better chance of solution. The translation process is usually carried out by means of the homology or homotopy groups of a topological space. Much of the book is therefore concerned with the construction of these algebraic invariants, and with applications to topological problems, such as the classification of surfaces and duality theorems for manifolds. Other important topics covered are homotopy theory, CW-complexes and the co-homology groups associated with a general Ω-spectrum.Dr. Maunder has provided many examples and exercises as an aid, and the notes and references at the end of each chapter trace the historical development of the subject and also point the way to more advanced results.”Throughout the text the style of writing is first class. The author has given much attention to detail, yet ensures that the reader knows where he is going. An excellent book.” — Bulletin of the Institute of Mathematics and Its Applications.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐A very interesting book which I enjoyed. I particularly found useful the “crash review” in algebra and analysis which functioned as a useful reference throughout the book.

⭐It is a decent book in algebraic topology, as a reference. At first, I found this textbook rather hard to read. Too many lemmas, theorems, etceteras. Three suggestions:1. Needs more pictures, especially for the simplicial homology Chapter.2. CW complexes should be covered before duality and not after.3. Needs more examples and exercises.Overall, the book is very good, if you have already some experience in Algebraic Topology. I found that the Croom’s book “Basic concepts of Algebraic Topology” is an excellent first textbook. Too bad it is out of print, since it is very popular, every time I get it from the library, someone else recalls it. The combination of these two books probably is the right thing to have: Maunder’s book picks up where Croom has left you.

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