Elements Of Algebraic Topology 1st Edition by James R. Munkres (PDF)

Description

Elements of Algebraic Topology provides the most concrete approach to the subject. With coverage of homology and cohomology theory, universal coefficient theorems, Kunneth theorem, duality in manifolds, and applications to classical theorems of point-set topology, this book is perfect for comunicating complex topics and the fun nature of algebraic topology for beginners.

User’s Reviews

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

⭐This is a user-friendly introduction to algebraic topology. While it assumes the reader is familiar with fundamental groups and covering spaces, its expositions of homology and cohomology theories are careful and detailed. Many worked examples and visual illustrations are included throughout this book. This is a salient feature of this book which is rather beneficial for the novice.

⭐Very good text if you want to learn Poincare duality and cohomology rings of spaces. Fundamental theorems of homological algebra such as Kunneth’s theorem and universal coefficient theorems are also thouroughly discussed. I think a good strategy is to use Hatcher’s book for Fundamental groups, covering spaces, homology and cohomology before Poincare duality and move to Munkres for cup product, cap product and Poincare duality.

⭐Algebraic topology is a tough subject to teach, and this book does a very good job. Some prerequisites, however, are essential:* point set topology (e.g. in Munkres’ Topology)* Abstract algebra* Mathematical maturity to be willing to follow a definition and argument even when it seems like a weird side-trackIn addition, this would not be the first book I would recommend to those interested in algebraic topology. First might be Massey’s “Algebraic Topology: and Introduction” that introduces the fundamental group (conceptually easier than homology and cohomology).At some point, however, a prospective student in topology will have to learn homological algebra and this provides the most concrete approach I know to the subject.Algebraic topology is a lot of fun, but many of the previous textbooks had not given that impression. This one does.

⭐This well written text is one of the standard references in algebraic topology courses because of its conciseness, and I find it very useful as a reference text.However I think it is a little incomplete because of several reasons.(1)It pays no attention to one basic concept of algebraic topology: the fundamental group.(2) It doesn’t cover ^Cech homology, important in other areas, like dimension theory for example.(3) It doesn’t stress the most important feature of algebraic topology: its connection to other areas of mathematics (analysis, differential geometry, etc.).(4) Its list of references is too short, and lacks almost completely HISTORICAL references which are always important to become an expert in any field.Conclusion: a good reference on homology and cohomology essentials, but not “the” reference on algebraic topology as a whole.

⭐It’s worth noting that there are quite a few in number of books out there on introductory (i.e. a first course in) alg. top.In particular, I should mention that the book by Rotman and sizeable portions of Bredon, “Geometry and Topology” can serve as good supplementary reading. I still don’t think pi_1 should have been left out; although one *could* refer to the prequel, there’s still more to be desired by way of completeness, if anything, as this book is intended for beginners. For instance, the relation between the fundamental group and the first homology group would have certainly shed some light on these seemingly (at first glance, anyway) disparate invariants (as it is heavy-going on the (co)homological apparatus altogether).Munkres is by no means encyclopaedic, which is good, in opposition to, say, Spanier or Whitehead, and certainly warrants attention to worked-out examples in detail and some (not-so) routine exercises which makes this book accessible to wider mathematical audiences wishing to learn a little about this fascinating subject.

⭐The best thing is that now it is available in Indian edition and hence can be bought. As usual, Munkres book is very easy to read and grasp/

⭐Reference book

Keywords

Free Download Elements Of Algebraic Topology 1st Edition in PDF format
Elements Of Algebraic Topology 1st Edition PDF Free Download
Download Elements Of Algebraic Topology 1st Edition 2018 PDF Free
Elements Of Algebraic Topology 1st Edition 2018 PDF Free Download
Download Elements Of Algebraic Topology 1st Edition PDF
Free Download Ebook Elements Of Algebraic Topology 1st Edition