After $K(1)$-localization, Adams's image of $J$ can be regarded as a transfer map: specifically, the transfer from the $C_2$-homotopy fixed points to the $\mathbb{Z}2^\times$-homotopy fixed points for $E_1$. This map corresponds to the canonical morphism $\Sigma^{-1} KO_2^\wedge \to L{K(1)} S^0$. We define transfer maps generally as duals to restriction maps. For arbitrary heights $n$ and closed subgroups $G \subset \mathbb{G}_n$ in the Morava stabilizer group, these transfer maps give analogs of the classical $J$ homomorphism at higher chromatic heights. This is joint work in progress with Ningchuan Zhang.