Comparing Periodic Point Invariants for Parameterized Families of Maps

We compare different periodic point invariants for families of maps parameterized over a compact manifold. Malkiewich and Ponto showed that, in the case of a single map, the Fuller trace is equivalent to the collection of Reidmeister traces of iterates. In this paper, we show that, in contrast to the case of a single map, the fiberwise Fuller trace is a strictly more sensitive invariant than the collection of fiberwise Reidemeister traces of iterates. This resolves a conjecture of Malkiewich and Ponto.