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.