The Transfer in Algebraic K-Theory and THH

Explore a comprehensive lecture on the transfer in algebraic K-theory and topological Hochschild homology (THH) delivered by Cary Malkiewich at the Hausdorff Center for Mathematics. Delve into the intricacies of ring maps, wrong-way transfer maps, and their applications in algebraic K-theory. Examine fundamental questions about these transfers and discover a program to address them using trace methods. Investigate the corresponding transfer on THH, particularly in the context of A-theory and its relation to stable maps of free loop spaces. Learn about splitting theorems, housing theorems, the Becker-Gottlieb transfer, and the cyclic bar construction. Analyze the A-theory inclusion conjecture, projection conjecture, and the advantages and disadvantages of various approaches. Gain insights into the trace and its implications for the study of fixed points in dynamical systems.

Introduction
Splitting theorem
Maps between K theory
Why study it
Housing theorem
The Becker Gottlieb transfer
The cyclic bar construction
Additional facts
A theory inclusion conjecture
Projection conjecture
Disadvantages
The trace
What happens to the trace