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The characteristic signatures of massive neutrinos on large-scale structure(LSS), if fully captured, can be used to put a stringent constraint on theirmass sum, $M_{\nu}$. Previous work utilizing N-body simulations has shown theMinkowski functionals (MFs) of LSS can reveal the imprints of massive neutrinoson LSS, provide important complementary information to two-point statistics andsignificantly improve constraints on $M_{\nu}$. In this work, we take a stepforward and apply the statistics to the biased tracers of LSS, i.e. thegalaxies, and in redshift space. We perform a Fisher matrix analysis andquantify the constraining power of the MFs by using the Molino mock galaxycatalogs, which are constructed based on the halo occupation distribution (HOD)framework with parameters for the SDSS $M_r < -21.5$ and -22 galaxy samples. Wefind the MFs give tighter constraints on all of the cosmological parametersthat we consider than the power spectrum. The constraints on$\Omega_{\mathrm{m}}, \Omega_{\mathrm{b}}, h, n_s, \sigma_8$, and $M_\nu$ fromthe MFs are better by a factor of 1.9, 2.9, 3.7, 4.2, 2.5, and 5.7,respectively, after marginalizing over the HOD parameters. Specifically, for$M_{\nu}$, we obtain a 1$\sigma$ constraint of 0.059 eV with the MFs alone fora volume of only $\left(1 h^{-1} \mathrm{Gpc}\right)^3$.

Probing massive neutrinos with the Minkowski functionals of the galaxy distribution