# Questions tagged [at.algebraic-topology]

Homotopy, stable homotopy, homology and cohomology, homotopical algebra.

5,694 questions
47 views

### Transgressive elements in Hopf algebra spectral sequence

Let $E^r$ be a commutative Hopf algebra homology spectral sequence over $\mathbb{Z}/p$, i.e. such that every sheet is a commutative Hopf algebra. I am struggling with proving (probably simple) fact -...
115 views

### Duality in Hopf algebras and Milnor-Moore paper

I am going through Milnor and Moore - On the structure of Hopf algebras (MSN) (I have already posted one question on that, another one is coming). My question is about Proposition 4.9, more ...
86 views

86 views

### When are cohomology operations determined by their action on coefficients?

It is well-known that K-theory operations are determined by the action on coefficients, but I don't know the right way to prove this fact, nor a reference for the same. On the other hand, clearly this ...
151 views

### Madsen-Tillmann spectrum $MTE$ of the group $E$ which is defined in Freed-Hopkins's paper

In Freed-Hopkins's paper, the group $E(d)$ is defined to be the subgroup of $O(d)\times\mathbb{Z}_4$ consisting of the pairs $(A,j)$ such that $\det A=j^2$, where $\mathbb{Z}_4=\{\pm1,\pm\sqrt{-1}\}$ ...
106 views

### homotopy MC element

A homotopy MC element is the Linfty analog of a Maurer-Cartan element for a Lie algebra. Where is anything written about homotopy MC elements as perturbations of strict MC elements?
256 views

111 views