Review: Introduction to Topological Manifolds

Introduction to Topological Manifolds by John M. Lee
My rating: 2 of 5 stars

The book is supposed to the prerequisites for author's (much better book) Introduction to Smooth Manifolds, however it doesn't really live up. The initial chapters on point set topology can be studied better from any standard textbook of Topology, and the later part about Algebraic Topology is much narrowly focused on being just a tool to study of manifolds that it misses much of the motivation and even important tools such as Excision Theorem. One is better off using An Introduction to Homological Algebra and Algebraic Topology: A Primer should one actually want to learn the subject as an end in itself. The only saving grace of the book is that it keep the focus on manifolds in the exercises, but one can directly jump to Introduction to Smooth Manifolds or An Introduction to Manifolds without much handicap.

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