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A Recognition Principle for Iterated Suspensions as Coalgebras Over the Little Cubes Operad by Flynn-Connolly, Oisín; Moreno-Fernández, José M.; Wierstra, Felix is a scholarly article available to read on EtoBox.

What is A Recognition Principle for Iterated Suspensions as Coalgebras Over the Little Cubes Operad about?

Our main result is a recognition principle for iterated suspensions as coalgebras over the little disks operads. Given a topological operad, we construct a comonad in pointed topological spaces endowed with the wedge product. We then prove an approximation theorem that shows that the comonad associated to the little $n$-cubes operad is weakly equivalent to the comonad $\Sigma^n \Omega^n$ arising from the suspension-loop space adjunction. Finally, our recognition theorem states that every little $n$-cubes coalgebra is homotopy equivalent to an $n$-fold suspension. These results are the Eckmann--Hilton dual of May's foundational results on iterated loop spaces.

Author

Flynn-Connolly, Oisín; Moreno-Fernández, José M.; Wierstra, Felix

Published

2022

Language

EN