All Questions
Tagged with hopf-algebras homotopy-theory
9
questions
4
votes
1
answer
109
views
Showing that the comultiplication map $E_*E\to E_*E\otimes E_*E$ is co-associative for a flat homotopy commutative ring spectrum
Let $(E,\mu,e)$ be a flat homotopy commutative ring spectrum, so we have an isomorphism
$$\Phi_E:E_*E\otimes_{\pi_*E}E_*E\to E_*(E\wedge E)$$
sending homogeneous elements $x:S^n\to E\wedge E$ and $y:S^...
0
votes
1
answer
57
views
Are any subalgebras of the steenrod algebra isomorphic to the group algebra over for some group? [closed]
Heading says it all. Wondering if there are any subalgebras of the steenrod algebra which are isomorphic as hopf algebras to $\mathbb{F}_2{G}$ for some group $G$? In particular interest to me are the ...
0
votes
1
answer
77
views
Compute $\operatorname{Ext}_{\mathcal{A}_2}^{s,t}(\mathcal{A}_2/ I(\mathcal A_2 . Sq^1), \mathbb F_2).$
I am trying to learn computations of the ASS by myself from "user's guide of spectral sequences" book and here is the thing I want to compute:
Compute $\operatorname{Ext}_{\mathcal{A}_2}^{s,...
user965463
4
votes
1
answer
503
views
Is the special orthogonal group really rationally homotopy commutative?
It is a classical result that the rational cohomology of $SO(n)$ is given by:
$$H^*(SO(2m); \mathbb{Q}) = \begin{cases}
S(\beta_1, \dots, \beta_{m-1}, \alpha_{2m-1}) & n = 2m \\
S(\beta_1, \dots, ...
- 54.7k
5
votes
1
answer
156
views
Why is the group $[\Sigma\Sigma X, Y]_{\ast}$ commutative?
Can anyone give a reference (or explain here), why the group $[\Sigma\Sigma X,Y]_*$ is commutative? How is it related to the fact that $\Sigma X$ is a co-H-space?
- 53
2
votes
0
answers
83
views
pontrjagin ring of the homology of iterated loop suspension
In The homology of C n+1 spaces, n>=0, F. Cohen, proof of Theorem 3.1 and proof of Theorem 3.2 (p. 228 - 243)
I totally do not understand the proofs of these two theorems from page 228 to page 243 ...
- 8,549
1
vote
1
answer
143
views
what means 'the realization of a topological category'
In the paper Homology Fibrations and the "Group-Completion"
Theorem. page 280 bottom line 10-bottom line 12, what means 'the realization of a topological category'?
- 8,549
5
votes
0
answers
801
views
Integral Homology of $BU$
We know that the integral cohomology of $BU$, $H^*(BU) = Z[c_1,c_2,...]$ where $|c_i| = 2i$ is the $i$th Chern class, with coproduct $\Delta c_i = \Sigma c_j\otimes c_{i-j}$.
And at almost ...
- 206
2
votes
1
answer
675
views
Computation of the hom-set of a comodule over a coalgebra: $Ext_{E(x)}(k, E(x)) = P(y)$.
First of all, since every other book somehow mentions that this is trivial, I apologize if it turns out that I am just misunderstanding something in the definitions. So here goes:
The motivation for ...
- 1,084