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• CommentRowNumber1.
• CommentAuthorDmitri Pavlov
• CommentTimeApr 4th 2021

Created:

## Idea

A generalization of homotopy groups.

## Definition

Given a finitely generated abelian group $A$ and $n\ge2$, we set

$\pi_n(X,A)=[P^n(A),X],$

where $P^n(A)$ is the $n$th Peterson space of $A$.

## References

• CommentRowNumber2.
• CommentAuthorUrs
• CommentTimeApr 5th 2021

Thanks for these pointers, hadn’t seen that before. For a moment I thought Peterson’s “Generalized Cohomotopy” might subsume twistorial Cohomotopy, but it doesn’t: He considers replacing spheres by homology spheres etc.

Regarding Neisendorfer’s terminology “with coefficients”: This seems a little unfortunate to me, as (co)homology “with local coefficient” is commonly understood to refer to twisted (co)homology, which doesn’t seem what this connects to?

Regarding the typesetting:

I have made some more of the technical terms hyperlinked (e.g. finitely generated) and added table of contents and floating context menu. Also made the page name singular, to comply with running convention. Last not least, I added pointer back to this entry here from “Related concepts” at homotopy group.

• CommentRowNumber3.
• CommentAuthorDmitri Pavlov
• CommentTimeApr 5th 2021
• (edited Apr 5th 2021)

Regarding Neisendorfer’s terminology “with coefficients”: This seems a little unfortunate to me, as (co)homology “with local coefficient” is commonly understood to refer to twisted (co)homology, which doesn’t seem what this connects to?