Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

Let $A=\oplus A_n$ be a primitively generated graded Hopf algebra, where each $A_n$ is a simplicial group. This allows us to define the homotopy group $\pi_*(A)$.

Question: is the graded Hopf algebra $\oplus \pi_*(A_n)\cong \pi_*(\oplus A_n)$ still primitively generated? Here * refers to a fixed positive integer.

Here is some context. Suppose one is given a filtration of a simplicial group. Then $A$ is often the associated graded algebra $E^0$ of this filtration. Usually then, for a spectral sequence, the $E^1$ will be $\pi_*(E^0)$.

Perhaps this question or similarly questions is generally known, and I would definitely be grateful for any references around this topic.

share|improve this question

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.