Topological Hochschild Homology and Fixed Point Invariants

Fixed point theorists have an array of invariants for determining if a self-map is homotopic to one without fixed points - most are elaborations of the classical Lefschetz invariant. In this talk, I'll discuss these invariants and show that they arise very naturally from topological Hochschild homology. Furthermore, the invariants are in the image on components of the cyclotomic trace from K-theory to THH. This suggests higher K-theory and THH as homes for more refined fixed-point data. In order to make the talk accessible I'll define the objects involved - a knowledge of the stable homotopy category is the only prerequisite. This is joint work with Kate Ponto.