  For any perfect fibration $E \rightarrow B$, there is a "free loop transfer
map" $LB_+ \rightarrow LE_+$, defined using topological Hochschild homology. We
prove that this transfer is compatible with the Becker-Gottlieb transfer,
allowing us to extend a result of Dorabia\l{}a and Johnson on the transfer map
in Waldhausen's $A$-theory. In the case where $E \rightarrow B$ is a smooth
fiber bundle, we also give a concrete geometric model for the free loop
transfer in terms of Pontryagin-Thom collapse maps. We recover the previously
known computations of the free loop transfer due to Schlichtkrull, and make a
few new computations as well.
