Algebraic Topology. Authors; (view affiliations) Edwin H. Spanier. Pages PDF · Homotopy and the Fundamental Group. Edwin H. Spanier. Pages this book is an exposition of the fundamental ideas of algebraic topology. DRM-free; Included format: PDF; ebooks can be used on all reading devices. Algebraic topology is the interplay between “continuous” and The second aspect of algebraic topology, homotopy theory, begins again with.
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Edwin H. Spanier. Algebraic Topology. Springer. Page 2. CONTENTS. INTRODUCTION. I. 1 Set theory 1. 2 General topology. 4! 3. Group theory. 6. 4. Modules. Textbooks in algebraic topology and homotopy theory. . 2That approach derives Poincaré duality as a consequence of Spanier-Whitehead and Atiyah. Spanier - Algebraic Topology () - Ebook download as PDF File .pdf) or view presentation slides online. Algebraic Topology.
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From the Back Cover The reader of this book is assumed to have a grasp of the elementary concepts of set theory, general topology, and algebra.
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This book was an incredible step forward when it was written A large number of other good to great books on the subject have appeared since then, so a review for current readers needs to address two separate issues: I took the course from Mr. Spanier at Berkeley a decade after the text was written. He was a fantastic teacher - one of the two best I've ever had the other taught nonlinear circuit theory.
We did NOT use this text, except as a reference and problem source.
He had pretty much abandonded the extreme abstract categorical approach by then. The notes I have follow the topical pattern of the book, but are so modified as to be essentially a different book, especially after covering spaces and the first homotopy group.
His statement was that his treatment had changed since the subject had changed significantly.
So much more has changed since then that I would not recommend this book as a primary text these days. So, why did I give it four stars? First, notice that it splits stylewise into three segments, corresponding the treatment of its material in a three quarter academic year.
The first three chapters intro, covering spaces, polyhedral have really not been superceded in a beginning text. Topics are covered very thoroughly, aiding the student new to the subject. The next three chapters homology are written much with much less explanation included - indeed, some areas leave much to the reader to discover and, consequently, aren't very helpful if the instructor doesn't fill in the details the text expects a rather rapid mathematical maturation from the first part - too much of a ramp in my opinion , but the text is comprehensive.
The last section homotopy theory, obstruction theory and spectral sequences should just be treated as a reference - it'd be hard to find all this material in such a compact form elsewhere and the obstruction theory section has fantastic coverage of what was known as of the writing of this book.
It's way too terse for a novice to learn from and there are some great books out there these days on the material. This book is a highly advanced and very formal treatment of algebraic topology and meant for researchers who already have considerable background in the subject.