Algebraic Topology

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As he explains in the preface, it would be pity if we miss the geometric intuition of the subject ( and it IS geometric), hence there are lots of diagrams in the book, which is a plus point. A couple of notes from courses by Mike Hopkins on elliptic cohomology and related stuff: 1995, 1999.

Finally, Deligne-Griffiths-Morgan-Sullivan's Real homotopy theory of Kähler manifolds: minimal models are things you can build at home! Revisions and Additions: I have made a number of small changes in the text itself in the years since the book was first published. The method of Groupes d'homotopie et classes de groupes abéliens might be considered old-fashioned, but it gives a strong taste of what localisation can achieve (e.

I feel that I should add my own answer here, now that I am more or less done reading homotopy and homology from Hatcher's text. Like I said earlier: one year of algebra won't necessarily prepare you for these routine abuses by the pros; you'll need two, or else tons of free time.

There are many possibilities out there, but a good one for beginners is Lee's Introduction to Topological Manifolds. Three papers that achieve perfect marriages of algebraic topology and differential geometry: Thom's Quelques propriétés des variétés différentiables founded cobordism theory. I know of one careless mistake every reader will catch and one subtle mistake almost no reader will catch). Lee is very careful and thorough in his presentation, which could help you with the gaps you have encountered. The readership of the n-Lab is not restricted to Algebraic Topologists of course, but the above list of notes would be useful to have readily available.

By using the Web site, you confirm that you have read, understood, and agreed to be bound by the Terms and Conditions. Some of the topics are: the shape of the universe, configuration spaces, digital image analysis, data analysis, social choice, and, of course, calculus. This book deals with a hard subject, but every effort has been made to explain and motivate the ideas involved before they are dealt with rigorously.