## EVENT DETAILS AND ABSTRACT

**Topology Seminar**
**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.

**Date:** Monday, March 06, 2006

**Time:** 4:10pm

**Where:** Lunt 104

**Contact Person:** Prof. Paul Goerss

**Contact email:** pgoerss@math.northwestern.edu

**Contact Phone:** 847-491-8544

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