# Tagged Questions

**20**

votes

**1**answer

1k 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 ...

**24**

votes

**8**answers

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

**5**answers

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 ...

**13**

votes

**10**answers

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

**3**answers

560 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.

**38**

votes

**7**answers

11k 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 ...

**38**

votes

**8**answers

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

**4**answers

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 ...

**25**

votes

**11**answers

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

**11**answers

8k 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, ...