Basic Algebraic Topology

"Thoroughly classroom-tested, this self-contained text teaches algebraic topology to students at the MSc and PhD levels, taking them all the way to becoming algebraic topologists. Requiring basic training in point set topology, linear algebra, and group theory, the book includes historical remarks to make the subject more meaningful to students. Also suitable for researchers, it provides references for further reading, presents full proofs of all results, and includes numerous exercises"--

"PREFACE This book is intended for a 2-semester first course in algebraic topology, though I would recommend not to try to cover the whole thing in two semesters. A glance through the contents page will tell the reader that the selection of topics is quite standard whereas the sequencing of them may not be so. The material in the first five chapters are very basic and quite enough for a semester course. A teacher can afford to be a little choosy in selecting exactly which sections (s)he may want to teach. There is more freedom in choice of materials to be taught from latter chapters. It goes without saying that these materials demand much higher mathematical maturity than the first five chapters. Also, this is where some knowledge of differential manifolds helps to understand the material better. The book can be adopted as a text for M.Sc./B.Tech./M.Tech./Ph.D. students. We assume that the readers of this book have gone through a semester course each in real analysis, and point-set-topology and some basic algebra. It is desirable that they also had a course in differential topology or concurrently study such a course but that is necessary only at a few sections. There are exercises at the end of many sections and at the end of first five chapters. Most of these exercises are part of the main material and working through them is an essential part of learning. However, it is not necessary that a student gets the right answers before proceeding further. Indeed, it is not a good idea to get stuck with a problem for too long--keep going further and come back to them later. There is a hint/solution manual for them at the end of the book for some selected exercises, especially for those which are being used in a later section, so as to make"--