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The polarization observables $T, E, P, H$, and $G$ in photoproduction of$\eta$ mesons off protons are measured for photon energies from threshold to$W=2400\,$MeV ($T$), 2280 MeV ($E$), 1620 MeV ($P, H$), or 1820 MeV ($G$),covering nearly the full solid angle. The data are compared to predictions fromthe SAID, MAID, J\"uBo, and BnGa partial-wave analyses. A refit within the BnGaapproach including further data yields precise branching ratios for the $N\eta$decay of nucleon resonances. A $N\eta$-branching ratio of $0.33\pm 0.04$ for$N(1650)1/2^-$ is found, which reduces the large and controversially discussed$N\eta$-branching ratio difference of the two lowest mass$J^P=1/2^-$-resonances significantly.

New data on $\vec{\gamma} \vec{p}\rightarrow \eta p$ with polarized photons and protons and their implications for $N^* \to N\eta$ decays