Search Results
| Search type | Search syntax |
|---|---|
| Tags | [tag] |
| Exact | "words here" |
| Author |
user:1234 user:me (yours) |
| Score |
score:3 (3+) score:0 (none) |
| Answers |
answers:3 (3+) answers:0 (none) isaccepted:yes hasaccepted:no inquestion:1234 |
| Views | views:250 |
| Code | code:"if (foo != bar)" |
| Sections |
title:apples body:"apples oranges" |
| URL | url:"*.example.com" |
| Saves | in:saves |
| Status |
closed:yes duplicate:no migrated:no wiki:no |
| Types |
is:question is:answer |
| Exclude |
-[tag] -apples |
| For more details on advanced search visit our help page | |
Results tagged with homotopy-theory
Search options questions only
not deleted
user 3995
Homotopy theory is an important sub-field of algebraic topology. It is mainly concerned with the properties and structures of spaces which are invariant under homotopy. Chief among these are the homotopy groups of spaces, specifically those of spheres. Homotopy theory includes a broad set of ideas and techniques, such as cohomology theories, spectra and stable homotopy theory, model categories, spectral sequences, and classifying spaces.
5
votes
0
answers
148
views
Topologies on the infinite join
Let $G$ be a topological group. Following Milnor one way of defining the total space of the universal bundle $EG$ of $G$ is to form the infinite join
$$
EG = G^{\ast \infty} = G \ast G \ast \dots
$$
e …
- 7,637
5
votes
0
answers
105
views
Classifying spaces of crossed modules
Let $\mathcal{G}$ be a strict topological $2$-group, i.e. a strict $2$-category with a single object, a space of invertible $1$-morphisms, a space of invertible $2$-morphisms and continuous structure …
- 7,637
6
votes
1
answer
419
views
Properties of coefficients of ring spectra
This is an awkwardly backwards question, but bear with me here: Suppose I have a graded ring $R$ with unit, which has an invertible element $u$ in degree $2$. The multiplicative formal group law $f(x …
- 7,637
5
votes
0
answers
212
views
G-spaces and SG-module spectra
This question is related to the one here, but has a slightly different angle.
Let $G$ be a topological group and let $X$ be a $G$-space. Taking the suspension spectrum $\Sigma^{\infty}_+ X$ (in my s …
- 7,637
10
votes
1
answer
647
views
Generalized Thom spectra
I am currently trying to wrap my head around all kinds of different definitions of the notion of (generalized) Thom spectrum. My setup is as follows: Suppose I have a commutative (symmetric) ring spec …
- 7,637
5
votes
1
answer
381
views
Mayer-Vietoris sequence for twisted R-homology
In this paper Ando, Blumberg, Gepner, Hopkins and Rezk define the twisted $R$-Homology of a ring spectrum $R$ together with a map $f \colon X \to R$-$Line$ to be
$$
R^f_n(X) =
\pi_0(map_R(\Sigma^nR, …
- 7,637
4
votes
0
answers
376
views
matrix ring spectra
I am trying to understand matrix ring spectra. Apparently, I have two different definitions of those and I did not manage to show that they are equivalent - maybe they even are not in the general case …
- 7,637
5
votes
1
answer
439
views
endomorphisms of modules over symmetric ring spectra
I have a probably very basic question about modules over symmetric ring spectra:
Let $R$ be a commutative symmetric ring spectrum and let $M$ and $N$ be module spectra over $R$. Moreover, let $\varp …
- 7,637
3
votes
1
answer
192
views
Sullivan's $H$-space equivalence between $G/PL[1/2]$ and $BO[1/2]$
There is a theorem by Sullivan of the following form:
Theorem: There is an equivalence of $H$-spaces
$$ G/PL[\tfrac{1}{2}] \simeq BO_{\otimes}[ \tfrac{1}{2} ]\ . $$
It can be found for example …
- 7,637
7
votes
2
answers
1k
views
Maps between classifying spaces
Let $G$ be a discrete group and let $BG \simeq K(G,1)$ be its classifying space. Let $H$ be a topological group with classifying space $BH$.
In case $H$ is also discrete, it was pointed out in the …
- 7,637
7
votes
1
answer
2k
views
Geometric realization of simplicial spaces and finite limits
Let $X_{\bullet}$ be a simplicial space and denote the (non-fat!) geometric realization by $\lvert X_{\bullet} \rvert$.
Does this geometric realization of simplicial spaces preserve finite limits …
- 7,637
2
votes
0
answers
439
views
Twisted product structure on product of Eilenberg-MacLane spaces
The product of Eilenberg-MacLane spaces $K(\mathbb{Z}/2,1) \times K(\mathbb{Z}/2,2)$ is an $H$-space with respect to a "twisted product structure", where you add the product of the first entries to th …
- 7,637
13
votes
1
answer
754
views
Units of MO and MU
Real (or complex) cobordism is described by a symmetric ring spectrum MO (or MU respectively) as explained in examples 2.8 and 2.9 here. Associated to such a ring spectrum $R$, we have a unit spectrum …
- 7,637
5
votes
1
answer
432
views
units in non-commutative ring spectra
Let $R$ be a connective (symmetric) ring spectrum. Let $GL_1(R)$ be the space of units of $R$, i.e. the union of the components of $\Omega^{\infty}(R)$ corresponding to the units of $\pi_0(R)$. $GL_1( …
- 7,637
11
votes
2
answers
1k
views
topological monoid from symmetric monoidal category
What is the standard reference for the fact that the classifying space of a strict monoidal category is a topological monoid with respect to the operation induced by the tensor product?
EDIT: The fir …
- 7,637