Whether youve loved the book or not, if you give your honest and detailed thoughts then people will find new books that are right for them. Localization, completion, and model categories chicago lectures in mathematics by may may, kathleen ponto isbn. Buy a concise course in algebraic topology chicago. More concise algebraic topology localization, completion, and. It covers most of what an introductory graduate course on the subject typically strives to discuss as well as many advanced topics, which is one reason it is among the standard, maybe even t. Topology is a fundamental tool in most branches of pure mathematics and is also omnipresent in more applied parts of mathematics. The chapters are laid out in an order that justifies the need for algebraic machinery in topology.
But if you want an alternative, greenberg and harpers algebraic topology covers the theory in a straightforward and comprehensive manner. The intent of the course was to bring graduate students who had completed a first course in algebraic topology to the point where they could understand research lectures in homotopy theory and to prepare them for the other, more specialized graduate courses being held in conjunction with the program. The more and more algebraic topology that i learn the more i continue to come back to hatcher for motivation and examples. Peter may, 9780226511832, available at book depository with free delivery worldwide. The fundamental group and some of its applications, categorical language and the van kampen theorem, covering spaces, graphs, compactly generated spaces, cofibrations, fibrations, based cofiber and fiber sequences, higher homotopy groups, cw complexes, the homotopy excision and suspension theorems.
More concise algebraic topology localization, completion, and model categories. More concise algebraic topology university of chicago. May algebraic topology is a basic part of modern mathematics, and some knowledge of this area is indispensable for any advanced work relating to geometry, including topology itself, differential geometry, algebraic geometry, and lie groups. Algebraic topology is a basic part of modern mathematics and some knowledge of this area is indispensable for any advanced work relating to geometry, including topology itself, differential geometry, algebraic geometry and lie groups. Peter may s a concise course in algebraic topology addresses the standard first course material, such as fundamental groups, covering spaces, the basics of homotopy theory, and homology and cohomology. More concise algebraic topology j peter may, kathleen ponto. Spaniers algebraic topology, mays a concise course in algebraic topology, and hatchers algebraic topology. Perhaps not as easy for a beginner as the preceding book. Localization, completion, and model categories chicago lectures in mathematics hardcover j. More concise algebraic topology localization, completion. In this sequel, may and his coauthor, kathleen ponto, cover topics that are essential for algebraic topologists and others interested in. Focusing more on the geometric than on algebraic aspects of the subject, as well as its natural development, the book conveys the basic language of modern algebraic topology by exploring homotopy, homology and cohomology theories, and examines a variety of spaces. As an algebraic topologist of algebraic bent, i also dont really like hatcher.
May with firm foundations dating only from the 1950s, algebraic topology is a relatively young area of mathematics. Peter mays a concise course in algebraic topology addresses the standard first course material, such as fundamental groups, covering spaces, the basics of homotopy theory, and homology and. This book provides a detailed treatment of algebraic topology both for teachers of the subject and for advanced graduate students in mathematics either. Illustrations note 117 line drawings, further reading. Algebraic topology is a basic part of modern mathematics, and some knowledge of this area is indispensable for any advanced work relating to geometry, including topology itself, differential geometry, algebraic geometry, and lie groups. This book is worth its weight in gold just for all the examples both throughout the text and in the exercises.
The serre spectral sequence and serre class theory 237 9. Textbooks in algebraic topology and homotopy theory. The adams spectral sequence, eilenbergmoore spectral sequences. May university of chicago press, 1999 this book provides a detailed treatment of algebraic topology both for teachers of the subject and for advanced graduate students in mathematics. More concise algebraic topology ebok may j p may, ponto. A concise course in algebraic topology currently unavailable. Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces. More concise algebraic topology cern document server. Buy a concise course in algebraic topology chicago lectures in mathematics book online at best prices in india on. The final four chapters provide sketches of substantial areas of algebraic. A list of recommended books in topology cornell university.
Pdf a basic course in algebraic topology download ebook for. Peter mays a concise course in algebraic topology addresses the standard first course material, such as fundamental groups. Ive seen portions of it, and it seems like it contains nice treatments of localizations and completions of spaces, model category theory, and the theory of hopf algebras. Everyday low prices and free delivery on eligible orders. Oct 29, 2009 the more and more algebraic topology that i learn the more i continue to come back to hatcher for motivation and examples. This book provides a treatment of algebraic topology both for teachers of the subject and for advanced graduate. The only prerequisites are some group theory, such as that normally contained in an undergraduate algebra course on the juniorsenior level, and a onesemester undergraduate course in general topology. While the book is indeed extremely terse, it forces the reader to thoroughly internalize the concepts before moving on. A concise course in algebraic topology chicago lectures in mathematics out of printlimited availability.
Peter may is the author of a concise course in algebraic topology 4. We give the most elementary treatment we know, making no use of simplicial techniques or model categories. Pdf a basic course in algebraic topology download ebook. This book provides a detailed treatment of algebraic topology both for teachers of the subject and for. A concise course in algebraic topology book, 2015 worldcat. There are numerous classical books devoted to algebraic topology of which we mention three.
Topology illustrated by peter saveliev intelligent perception the text follows the content of a fairly typical, twosemester, first course in topology. It covers most up to date essentials and is the must for resrarchers. Buy a concise course in algebraic topology chicago lectures. The fundamental group and some of its applications, categorical language and the van kampen theorem, covering spaces, graphs, compactly generated spaces, cofibrations, fibrations, based cofiber and fiber sequences, higher homotopy groups, cw complexes, the homotopy excision and suspension. I think the people who like it most tend to be very geometrically minded and dont mind a little lack of rigor. The topological classification of stratified spaces. Hatchers algebraic topology is a perfectly fine book. There are very few textbooks that treat fundamental topics beyond a first course, and many topics now essential to the field are not treated in any textbook. A concise course in algebraic topology chicago lectures in mathematics 9780226511832 by may, j. Reliable information about the coronavirus covid19 is available from the world health organization current situation, international travel. This book really does pack quite a punch from a thoroughly modern point of view.
The word on the street is that peter may in collaboration with kate ponto is writing a sequel to his concise course with a title like more concise algebraic topology. Algebraic topology a first course graduate texts in. Mays book a concise course in algebraic topology is a superb demonstration of this. Peter mays a concise course in algebraic topology addresses the. Localization, completion, and model categories ebook written by j. Is allen hatchers algebraic topology a good introduction. This book provides a concise introduction to topology and is necessary for courses in differential geometry, functional analysis, algebraic topology, etc. Kathleen ponto is assistant professor of mathematics at the university of kentucky. The main topics covered include the classification of compact 2manifolds, the fundamental group, covering spaces, and singular homology theory. Peter mays a concise course in algebraic topology addresses the standard first course material. A concise course in algebraic topology download link. Most chapters end with problems that further explore and refine the concepts presented. With firm foundations dating only from the 1950s, algebraic topology is a relatively young area of mathematics. Peter mays a concise course in algebraic topology addresses the standard first course material, such as fundamental.
The basic goal is to find algebraic invariants that classify topological spaces up to homeomorphism, though usually most classify up to homotopy equivalence although algebraic topology primarily uses algebra to study topological problems, using topology to solve algebraic problems. This classic textbook in the graduate texts in mathematics series is intended for a course in algebraic topology at the beginning graduate level. Algebraic topology and a concise course in algebraic topology in this series. In this sequel, may and his coauthor, kathleen ponto, cover topics that are essential for algebraic topologists and others interested in algebraic topology, but that are not treated in standard texts. Are there better algebraic topology books than hatcher s. Unfortunately, you dont see many texts like these in print anymore. Numerous and frequentlyupdated resource results are available from this search.
The subject matter of algebraic topology, by its very nature, consists of plenty of geometric ideas and a hoard of algebraic structures. More concise algebraic topology j peter may, kathleen. It would be worth a decent price, so it is very generous of dr. Peter may is professor of mathematics at the university of chicago and the author of several books, including a concise course in algebraic topology and simplicial objects in algebraic topology, both in the chicago lectures in mathematics series. In any event,its very daring to write an algebraic topology problem course,especially one thats supposed to be somewhat more advanced then the usual books. For undergraduate algebraic topology, i like the end of. Peter mays a concise course in algebraic topology addresses the standard first course material, such as fundamental groups, covering spaces, the basics of homotopy theory, and homology and cohomology. A concise course in algebraic topology edition 2 by j. A guiding principle of the text is that algebraic machinery must be introduced only as needed, and the topology is more important than the algebraic methods.
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