On the Wreath Transfer in the Homology of Symmetric Groups
发布时间：2026年10月27日
浏览次数：7
发布者: He Liu
主讲人： 李德洲（数学中心）
活动时间： 从 2026-10-30 15:00 到 16:00
场地： 北京国际数学研究中心，镜春园78号院（怀新园）77201室
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.
