On the Wreath Transfer in the Homology of Symmetric Groups -

On the Wreath Transfer in the Homology of Symmetric Groups

Time: 2026-10-27 Published By: He Liu

Speaker(s): Dezhou Li (BICMR)

Time: 15:00-16:00 October 30, 2026

Venue: Room 77201, Jingchunyuan 78, BICMR

For an odd prime $p$, we give an explicit formula for the wreath transfer $tr: H_*(\Sigma_{p^2}) \rightarrow H_*(\Sigma_p \wr \Sigma_p)$ associated with the standard inclusion $\Sigma_p \wr \Sigma_p$ to $\Sigma_{p^2}$. The proof is a direct algebraic computation, using Cartan's classical double-coset formula together with a generating-function argument. As an immediate consequence, we obtain an elementary proof of the validity of the mixed Adem relations in Goodwillie calculus.