In this talk we give a description of a lift of the Dennis trace and the characteristic polynomial to TR using the framework of bicategories and bicategorical traces. The goal of this construction is to demonstrate that TR is the natural home of the characteristic polynomial, and to give a natural and clean demonstration of this fact. The overarching goal of this project is to show that most traces have natural interpretations in terms of bicategories; time permitting, we will show that the Reidemeister trace associated to a self-map of a finite CW complex is another example of such a construction.
Warning: the talk was delivered by writing live on a tablet’s whiteboard. Posted as a “slides” below you will find a pdf obtained by merging a writeup of the talk together with what was actually written on the tablet and appears on the video. The speaker has asked us to make very clear that the writeup is “very messy and rough, and was intended as the rough notes for the talk“.