Algebraic Topology

Product Information

I'm hoping that will not only expose me to the cutting edge,but allow me to work with one of the greats. Now it is true that he doesn't assume too much background in abstract algebra (knowing the basics of groups, rings, and modules is more than sufficient). The first equation for polytropic index n ≠–1, ±∞ depends on five free parameters, while the other equation is for, n ＝ ±∞ and depends on three free parameters.

Before introducing a concept, he will motivate it by proper examples and proves theorems after stating some interesting consequences hence great for self study. This introductory text is suitable for use in a course on the subject or for self-study, featuring broad coverage and a readable exposition, with many examples and exercises. Whether this is a good book or a bad book depends on your background, what you hope to gain from it, how much time you have, and (if your available time is not measured in years) how willing you are to take many things on faith as you press forward through homology, cohomology and homotopy theory. Long story short I think once you have learned the contents of Chapters 0 and 1 in Hatcher from some source, you can just read the rest of it.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. Homologie singulière des éspaces fibrés has as clear and economical an account of spectral sequences as I've seen anywhere. Often done with simple examples, this gives an opportunity to get comfortable with them first and makes this book about as readable as a book on algebraic topology can be.

such that f ′ ∘ f ≃ 1 X {\displaystyle f' \circ f \simeq 1_X} and g ′ ∘ g ≃ 1 Y {\displaystyle g' \circ g \simeq 1_Y} then this means we have homotopies Φ : X × I → X {\displaystyle \Phi : X \times I \to X} and Γ : Y × I → Y {\displaystyle \Gamma : Y \times I \to Y} such that Φ 0 = 1 X {\displaystyle \Phi_0 = 1_X} , Φ 1 = f ′ ∘ f {\displaystyle \Phi_1 = f' \circ f} , Γ 0 = 1 Y {\displaystyle \Gamma_0= 1_Y} , Γ 1 = g ′ ∘ g {\displaystyle \Gamma_1 = g' \circ g} (along with two more homotopies going in the other direction). A unique feature of the book is the inclusion of many optional topics which are not usually part of a first course due to time constraints, and for which elementary expositions are sometimes hard to find.BibTeX key MR1867354 entry type book address Cambridge year 2002 pages xii+544 publisher Cambridge University Press mrreviewer Donald W.