I am looking for the most basic but rigorous to some extent book on Algebraic topology out there.
Rotman is good. I think Hatcher is really hard to follow, though others like him.
Well, Munkres has been written for undergrads. the first part of the book is general topology and the second is algebraic topology.
Greenberg and Harper has the virtue of not using too many words
I think Hatcher's beautiful book is an important addition to the roster, but probably that it is intended for students who aren't feeling overwhelmed.
I've got Greenberg and Harper beside me. It looks formidable/impossible due to as you say not many words.
I'm looking for a dummies book, if there is one.
Aren't you a physcist? If so which area in physics? You seem to be keen with maths as well?
I would try Munkres.
i think you are looking for "Algebraic Topology: An Introduction" by William S. Massey
A classic in Dover reprint is Hocking and Young's "Topology". It is a clear introduction to point-set topology and algebraic topology at the level of a first undergraduate course on topology. It is similar in coverage to Munkres but I find H&Y to be more readable.
A cheap and cheerful introduction is Wallace's Intro to Algebraic Topology (Dover, ~£7). I ordered a handful of Dover books a little while ago on subjects I was unfamiliar with. After some very casual reading, the book has managed to provide me with a grounding in basic algebraic topology. Lots of nice pictures, and the exercises are very routine (so much so that in many cases you needn't put pen to paper).
ah, i meant A Basic Course in Algebraic Topology by William S. Massey, it is a revised and enhanced version of Algebraic Topology, an Introduction....
Btw, Munkres is an introduction to Algebraic topology.
After his take, one procceeds to Edwin Spanier (Though I haven't yet, and probably will not have time either way to finish Munkers and even starting Spanier).
william massey is one of the very few writers on advanced mathematics i know of who has always been understandable to the beginner.
i have not read his book recommended above including an introduction to singular homology (basic course...) but in grad school his little book on the fundamental group was the only one i could understand, and later his book which serves as the first 5 chapters of "basic course.." on both fundamental group and classification of two manifolds, seemed like a playtime book.
homology theory is notoriously hard to make understandable, and i would suggest looking at books by fulton, and the chapter in spivak's differential geometry book vol 1, as well.
i also recommend massey's book on differential topology, first steps.
hocking and young is a very old fashioned book, which has much good classical material, but more on point set topology than you need in algebraic topology, and the point of view is not at all up to date.
all the professional algebraic topologists here love to use hatcher in their courses, but to me it is not that appealing. i liked vick, homology theory, as a student also.
spanier is very detailed and formidable, but excellent for those wishing to become professionals.
for beginners massey is hard to beat. if you read german there is also a fine book by artin and braun, which was apparently the model for the first part of greenberg's book.
Should be Wallace; "Differential Topology, First Steps"?
Massey's "Basic Course..." is very nice indeed and almost certainly a better recommendation than Hocking and Young.
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