We have performed a multichannel-dispersion-relation calculation of low-energy ($E_{\gamma }\lesssim 450$ MeV) pion photoproduction. We are able to fit the present $\gamma p$ data along with the less-well-known $\gamma n\to {\pi }^{-}p$ data without the introduction of an $I=2\mathrm{}$ electromagnetic current. Predictions for the reaction $\gamma n\to {\pi }^{0}n$ are made. Parameters are introduced to describe the photoproduction Born terms for the inelastic hadronic channels. We find that through the rescattering integrals, the inelastic effects strongly influence the $\gamma N\to \pi N$ amplitudes even at low energy (in particular, in the $E_{0+}$ and $M_{1-}$ multipoles).

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