Introduction to Topological Manifolds (Graduate Texts in Mathematics Book 202) 2nd Edition by John Lee (PDF)

Description

This book is an introduction to manifolds at the beginning graduate level, and accessible to any student who has completed a solid undergraduate degree in mathematics. It contains the essential topological ideas that are needed for the further study of manifolds, particularly in the context of differential geometry, algebraic topology, and related fields.Although this second edition has the same basic structure as the first edition, it has been extensively revised and clarified; not a single page has been left untouched. The major changes include a new introduction to CW complexes (replacing most of the material on simplicial complexes in Chapter 5); expanded treatments of manifolds with boundary, local compactness, group actions, and proper maps; and a new section on paracompactness.

User’s Reviews

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

⭐Best book of topographical manifold .

⭐Lee’s book is very good, and I am using it for self-study, which is why I give 5 stars (for content).EDIT May 2019: Springer uses print-on-demand technology, hence the inferior printing quality. Don’t know what can be done about it.

⭐Good first read through for anyone beginning a study of topological concepts. Anyone having trouble with the preliminary chapters might try this book in conjunction with Munkres and Ken Ross’s ‘Elementary Analysis.’

⭐The author has done an outstanding job writing this book. Highly recommend this book.

⭐The book is formal, which can be a bad thing, but the book is filled with discussions / intuition & nice drawings to make it clear to read.The second half of the book is on Algebraic Topology and covers topics in a first course on Algebraic Topology.Overall I highly recommend reading this book, especially for someone who knows the basics of point set topology.

⭐Just a quick note:I say “requires some prior experience” because with some knowledge already (say from “Introduction to Topology, Bert Mendelson”) the book makes a lot more sense and can be read a lot faster. This is a great book – IF – you already know what a metric space is, and have dealt with them before, and know that metric spaces induce (Hausdorff) topologies.It’s also very weak (doesn’t cover) the functional analysis side of topology. All inner products induce normed spaces and all normed spaces induce metric spaces, as it doesn’t cover those this isn’t a surprising absence, but as such T1,T2,T3 and T4 spaces (I think T2 is Hausdorff, that’s mentioned but the others are not I think….) are not mentioned. This is not a bad thing! For that I recommend one looks at: “Introduction to Topology” by “Gamelin and Greene”.This is a very topology-only book. On with the review!This book is a really good “Topology” book, it’s also very accessible, some of the things in the GTM series I pick off the library shelf thinking “This will be good” and then it hits me with some sort of intellectual shovel and puts me back in my place: of not being worthy of the book.If you’re studying topology at university, you’ll want this book, it DOES NOT really cover metric spaces (if at all) so be warned! I really like Lee’s (I feel so grown up, using the second name of authors like this!) style and have adopted his style guide (search for “John Lee PDF” to find it) for many things. It’s very clear and consistent, there’s rarely if ever any ambiguity.I also like Lee (doing it again!) because he is like me when it comes to definitions, and doesn’t mind multiples, for example, he distinguishes between retract, deformation retraction, and a strong deformation retraction, however ANOTHER great Topology book, like say by James R. Munkres, or even Hatcher’s “Algebraic Topology” call a strong deformation retract a “deformation retract” and never deal with what Lee calls just a “deformation retract”.There’s only one case where he hasn’t opted for “the most abstract series of definitions” and that’s when he defines the Adjunction space of two topologies and a function from a subspace. He requires the subspace be closed, this isn’t needed.But anyway, it’s a very good book. I’ve cross-posted this on a few entries for what look like the second edition of this book, but just to confirm:This review is for the SECOND EDITION of Introduction to Topological Manifolds.If you’re studying topology this is the one book you’ll need, however for a second-year introduction building on metric spaces I really recommend:”Introduction to Topology” by Bert Mendelson, this is a nice metric spaces intro leading into Topology, then this book builds on all that for a complete course.The joint third books I’d recommend to couple with this are:1) Introduction to Topology – Gamelin and Greene – this is a small reference book, of similar level, it introduces some differing terminology and constructions which one ought to be aware of2) Topology – James R. Munkres – a very good book on the same subject, I don’t always agree with his conventions and the writing is a little less formal (Lee has a strict style guide)I’m not entirely sure what to put. If you’re leaving for a while and taking Topology in say a 3rd year mathematics course, this is a superb book. Any questions, please just ask and I’ll do what I can to help.

⭐El contenido del libro es excelente, lo recomiendo ampliamente. Desafortunadamente, la impresión deja mucho que desear (tengo otro libro de la misma editorial pero vendido por amazon DE y la diferencia en la calidad es abismal). Ojalá los estándares de calidad americanos mejoraran, ya que no son libros baratos.Everything someone needs to know about topology when just trying to learn enough to understand manifolds. Lee has an amazing ability to make difficult concepts easy and intuitive and I wish I had such amazing professors when I was in University.

⭐A reference book for a serious introduction to Manifolds. Suited for an upper undergraduated and first-year graduate course both in Topology and Differentiall Geometry. But also for a self-study, assuming only some elementary calculus and linear geometry.

⭐Lucid suitable for self study.

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