20
votes
1answer
978 views

Why not a Roadmap for Homotopy Theory and Spectra?

MO has seen plenty of roadmap questions but oddly enough I haven't seen one for homotopy theory. As an algebraic geometer who's fond of derived categories I would like some guidance on how to build up ...
23
votes
8answers
3k views

An “advanced beginner's” book on algebraic topology?

It has so happened that I have come this far knowing nothing on the subject of algebraic topology (as in homology theories of topological spaces and their applications). I've decided to finally read ...
18
votes
5answers
2k views

A toolbox for algebraic topology

This question has a very general part and a rather concrete part. General: When one wants to prove something in algebraic topology (actually in all parts of mathematics) one obviously needs some ...
12
votes
9answers
3k views

Good book on Riemann surfaces and Galois theory?

I'm supervising an undergraduate project on Galois theory and covering spaces. I want to have him read about the fact that from a branched cover of a Riemann surface you get an extension of its field ...
4
votes
3answers
549 views

What is the best paper or book studying the P homomorphism, J homomorphism and Hopf invariant in Homotopy theory?

I want to study P & J homomorphisms and Hopf invariant in Homotopy theory. I have some paper, but I don't know what is first and what is nice. Please recommend to me.
35
votes
7answers
10k views

Is Mac Lane still the best place to learn category theory?

For a student embarking on a study of algebraic topology, requiring a knowledge of basic category theory, with a long-term view toward higher/stable/derived category theory, ... Is Mac Lane still ...
35
votes
8answers
3k views

Natural transformations as categorical homotopies

Every text book I've ever read about Category Theory gives the definition of natural transformation as a collection of morphisms which make the well known diagrams commute. There is another possible ...
12
votes
4answers
3k views

Textbook or lecture notes in topological K-Theory

I am looking for a good introductory level textbook (or set of lecture notes) on classical topological K-Theory that would be suitable for a one-semester graduate course. Ideally, it would require ...
24
votes
11answers
9k views

Algebraic Topology Beyond the Basics:Any Texts Bridging The Gap?

Peter May said famously that algebraic topology is a subject poorly served by it's textbooks. Sadly,I have to agree. Although we have a frieghtcar full of excellent first-year algebraic topology ...
27
votes
11answers
7k views

Homological Algebra texts

I would like to hear the communities' ideas on good Homological Algebra textbooks / references. The standard example is of course Weibel (which I'll leave for someone else to describe). As usual, ...