The fiberwise Fuller trace obstruction conjecture

Let $B$ be a finite-dimensional cell complex, and let $E\to B$ be a smooth closed manifold bundle with fiber $M$ of dimension at least $3+\dim B$. Let $f\colon E\to E$ be a family of endomorphisms over $B$. Fiberwise Fuller trace conjecture. The fiberwise Fuller trace is the complete obstruction to removing $n$-periodic points from $f$. This is presented as the fiberwise analogue of the classical obstruction theorem, but the paper states that proving it will require substantially different techniques and leaves it for future work.