dalam airwania upanjang yang. AN INTRODUCTION TO ALGEBRAIC TOPOLOGY by Joseph , Graduate Texts in Mathematics , Springer- Verlag. Joseph J. Rotman. An Introduction to Algebraic Topology. With 92 Illustrations. Springer-Verlag. New York Berlin Heidelberg London Paris. Tokyo HongKong. An Introduction to Algebraic Topology by Joseph J. Rotman, , available at Book Depository with free delivery worldwide.
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I’m comfortable with general topology and category theory, but I haven’t had much exposure to algebraic topology beyond the basics of the fundamental group oid and de Rham cohomology. In particular, I’d like to learn about the various homology and cohomology theories. I suggest Peter May’s Concise course on algebraic ihtroduction.
An Introduction to Algebraic Topology : Joseph J. Rotman :
You will find e. Rotman’s An Introduction To Algebraic Topology is a great book that treats the subject from a categorical point of view.
Even just browsing the table of contents makes this clear: Chapter 0 begins with a brief review of categories and functors.
Natural transformations appear in Chapter 9, followed by algebrauc and cogroup objects in Chapter The aspect I like most about this book is that Rotman makes a clear distinction between results that are algebraic and topological.
Spanier’s book is relatively old so I know it does not quite answer your questionbut excellent. It uses category theory from the get-go.
Aglebraic “Categorical homotopy theory” is very well-written, though it may be a bit too advanced if you hadn’t seen a bit of algebraic topology already. Riehl’s book is focused on the categorical aspect via Quillen model structures.
A major and important area of algebraic topology. The categorical requirements for appreciating the Quillen machinery are not modest, and the book does a great job presenting all that is needed.
Having said all that, if you find a text that you like but which avoids the category theoretic language, then you should be able to quite easily fill-in the gaps on your own. Simply consult online sources e.
In an introductory text you will probably cover the fundamental group oidVan Kampen’s Theorem, some higher homotopy groups, and some homology. Chapter 1 is called Categories and Functorsso that’s a good start.
Home Questions Tags Users Unanswered. An introduction to algebraic topology from the categorical point of view Ask Question. I highly recommend Tammo Tom Dieck’s book, which takes a categorical approach even if it doesn’t always explicitly use categorical language.
An Introduction to Algebraic Topology – Joseph Rotman – Google Books
I like Tom Dieck’s book as well,but I think it’s too sophisticated for any but the best students. To effectively read it,one needs to be VERY comfortable with basic algebra up to and including R-modules and basic category theory in addition to some background in point set topology, the fundamental group and homotopy theory.
I think this is a tall order for most beginning graduate students in the U. I also think it’s too dry and abstract,completely disconnecting the material from it’s geometric sources. In a sense,it’s the “anti-Hatcher”. May has the same problem,only not as bad. Martin Brandenburg k 13 I think this is just what I was looking for. Students that master Rotman will be well-equipped to move on to more sophisticated monographs and research papers. Rotman is one of our very best textbook authors. Filling in “on your own” isn’t always so easy; language dictates how people think, and it isn’t all that uncommon to see a text have tell you things about products, but remain silent about the corresponding statement for equalizers, so filling in the gap requires you to actually develop that part of the theory yourself or discover relevant counterexamples on your own.
Qiaochu Yuan k 32 I have to mention that the notion of the fundamental groupoid on a set of base points has been well supported by A. Grothendieck in his “Esquisse d’un Programme” rohman will be found in texts in English on topology only in the book “Topology and Groupoids” -do a web search though that book contains no homology. Sign up or log in Sign up using Google. Sign up using Facebook. Sign up using Email and Password.
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An Introduction to Algebraic Topology