EVENT DETAILS AND ABSTRACT

Title: Factoring the Becker-Gottlieb Transfer through the Trace map
Speaker: Professor Mark Johnson
Speaker Info: Penn State Altoona
Brief Description:
Special Note:
Abstract:

The Becker-Gottlieb transfer of a fibration $p:E \to B$ is a stable map in the other direction, $\tau(p):Q(B_+) \to Q(E_+)$. Associated to the same fibration one also has the algebraic K-theory transfer $p^*:Q(B_+) \to A(E)$, whose target is Waldhausen's algebraic K-theory of the total space. Finally, one always has the Trace map $tr:A(E) \to Q(E_+)$ and the claim is that $tr \circ p^* \simeq \tau(p)$ for compact ANR fibrations. The proof is surprisingly clean, thanks to the axiomatic description of $\tau(p)$ for this type of fibration given by Becker and Schultz. We simply verify these axioms hold for our composite $tr \circ p^*$, although this requires us to work with relative versions of all of the above constructions.