Up to homotopy, the Lefschetz number and its refinement to the Reidemeister trace capture the essential information about fixed points of an endomorphism. These invariants can be applied to iterates of an endomorphism to describe periodic points, but in this case they provide far less complete information.

I will describe an approach to refining these invariants through refinements of the associated symmetric monoidal and bicategorical traces. This gives richer invariants that also apply to endomorphisms of spaces with more structure (such as bundles).

This work is joint with Cary Malkiewich.

Pretalk at 3:15 pm in Hylan 306.