Revisions and Additions: I have made a number of small changes in the text itself in the years since the book was first published. This textbook on elementary topology contains a detailed introduction to general topology and an introduction to algebraic topology via its most classical and elementary segment centered at the notions of fundamental group and covering space. Yes, I would rate its difficulty a notch above your typical introductory text in, say, analysis, algebra or point-set topology. In this book the authors present the technical tools needed for proving rigorously the classification theorem, give a detailed proof using these tools, and also discuss the history of the theorem and its various proofs. Images Donate icon An illustration of a heart shape Donate Ellipses icon An illustration of text ellipses.

You can think of that discussion of Hatcher as a "prerequisite quiz" which tests whether you have learned what you need to learn about homotopies. where he says that the three graphs are homotopy equivalent because they are deformation retract of a disk with two holes. Both have a number of misprints, but are essential reading if one wants to get into modern stable homotopy theory. There are many possibilities out there, but a good one for beginners is Lee's Introduction to Topological Manifolds.To save this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. We don’t share your credit card details with third-party sellers, and we don’t sell your information to others. Otherwise, while you may be able to fool yourself into thinking you know what the hell is going on, you won't really have anything but a superficial grasp of the basics. All posts and comments should be directly related to mathematics, including topics related to the practice, profession and community of mathematics. The only thing that comes to mind that might be controversial is the usage of Delta complexes, which I’ve heard is seldom used elsewhere and doesn’t do much to simplify material.

I'll close this box and throw it open to the floor by sharing what may be the first such textbook available as a massive set of online notes. Please also list any non-financial associations or interests (personal, professional, political, institutional, religious or other) that a reasonable reader would want to know about in relation to the submitted work.And I think it is indisputable that you simply will not be able to find a book that more richly and effectively conveys the intuitive geometric content of this subject.

He doesn't walk you through every tedious step, so at the beginning you will have to read more slowly until your mind gets smarter about filling in the blanks--which it will learn to do if you put in the time.Although I think Hatcher's book is littered with great, well-thought out examples, I personally didn't like it. As noted on the page itself, however, the proof contains methodologies borrowed from other sources which, at face value, seem overly complicated. I just wanted to add that I learned a big part of what I know about homology, cohomology and homotopy theory from Hatchers book and I think that that part of the book is a great source for that.