Abstract

We extend earlier work of Waldhausen which defines operations on the algebraic $K$-theory of the one-point space. For a connected simplicial abelian group $X$ and symmetric groups ${\Sigma }_n$, we define operations ${\theta }^n:A\left(X\right)\to A\left(X\times B{\Sigma }_n\right)$ in the algebraic $K$-theory of spaces. We show that our operations can be given the structure of $E_{\infty }$-maps. Let ${\varphi }_n:A\left(X\times B{\Sigma }_n\right)\to A\left(X\times E{\Sigma }_n\right)\simeq A\left(X\right)$ be the ${\Sigma }_n$-transfer. We also develop an inductive procedure to compute the compositions ${\varphi }_n\circ {\theta }^n$, and outline some applications.

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Mathematical Subject Classification 2010

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