Periodic Points and Topological Restriction Homology

We answer in the affirmative two conjectures made by Klein and Williams. First, in a range of dimensions, the equivariant Reidemeister trace defines a complete obstruction to removing n-periodic points from a self-map f. Second, this obstruction defines a class in topological restriction homology. We prove these results using duality and trace for bicategories. This allows for immediate generalizations, including a corresponding theorem for the fiberwise Reidemeister trace.