Tagged Questions

6
votes
3answers
59 views

introductory reference for Hopf Fibrations

I am looking for a good introductory treatment of Hopf Fibrations and I am wondering whether there is a popular, well regarded, accessible book. ( I should probably say that I am just starting to ...
2
votes
1answer
49 views

reference request: Postnikov towers for non-simply-connected spaces

I've read that for a space $X$ which is connected but not necessarily simply-connected, we can no longer obtain the $n^{\rm th}$ layer $P_nX$ of the Postnikov tower for $X$ as the pullback of a ...
2
votes
0answers
39 views

Equivariant homotopy equivalence of based loop group

Consider a compact, connected, simply connected Lie group $G$ and consider $S^1$ as an additive group. Let $\Omega G = \{ \gamma: S^1 \to G: \gamma(0) = e_G\}$ be the corresponding based loop group of ...
2
votes
1answer
84 views

Are strongly close maps homotopic?

While reading about various results related to density of smooth functions in the space of continuous functions with strong topology, I've got the impression that it is a general fact that for any ...
9
votes
1answer
357 views

Courses on Homotopy Theory

This autumn I'm considering taking an "advanced" reading course in Algebraic Topology, more specifically homotopy theory. I could extend this reading course over a year and wouldn't mind studying hard ...
9
votes
1answer
220 views

What are $E_\infty$-rings?

I've been working with DG-algebras for the last year, and was able to obtain using them some nice commutative homological algebra results. However, I keep hearing about a (more general???) concept of ...
7
votes
3answers
278 views

What is combinatorial homotopy theory?

Edit: After a discussion with t.b. we agreed that this question aims to a different answer from this one, for more information you can read the comment below. Many times I've heard people ...
3
votes
1answer
138 views

Exact Constructions of Homotopy Fiber and Cofiber of Spectra

Given a map of spectra (pick whatever category you want), $f:X\to Y$, what are the exact constructions of the fiber and cofibers of this map? Does this depend in any deep way upon the category or ...
15
votes
1answer
491 views

Brave New Number Theory

I suppose this is an extremely general question, so I apologize, and perhaps it should be deleted. On the other hand it's an awesome question. Is it clear exactly how much (assumedly algebraic) ...
3
votes
2answers
221 views

Good Reference for Spanier-Whitehead duality?

Does anyone know of a good book that explains Spanier-Whitehead duality (other than Adams)? Thanks Jon
10
votes
2answers
307 views

Introductory book for homotopical algebra

I'm interested in learning homotopical algebra (by which I mean: model categories, simplicial methods, etc.) However, I've been unable to make heads or tails of any of the "standards" ...
4
votes
0answers
295 views

Good Reference for Large Cardinals/Homotopy Theory

I'm planning on attending a conference in Barcelona in September called "Large Cardinal Methods in Homotopy Theory" and want to try to be as prepared as I possibly can. Are there good references for ...