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We derive cosmological constraints on the matter density, \om, and theamplitude of fluctuations, \sig, using $\mathtt{GalWCat19}$, a catalog of 1800galaxy clusters we identified in the Sloan Digital Sky Survey-DR13spectroscopic data set using our GalWeight technique to determine clustermembership \citep{Abdullah18,Abdullah19}. By analyzing a subsample of 756clusters in a redshift range of $0.045\leq z \leq 0.125$ and virial masses of$M\geq 0.8\times10^{14}$ \hm ~with mean redshift of $z = 0.085$, we obtain \om~$=0.310^{+0.023}_{-0.027} \pm 0.041$ (systematic) and \sig~$=0.810^{+0.031}_{-0.036}\pm 0.035$ (systematic), with a cluster normalizationrelation of $\sigma_8= 0.43 \Omega_m^{-0.55}$. There are several unique aspectsto our approach: we use the largest spectroscopic data set currently available,and we assign membership using the GalWeight technique which we have shown tobe very effective at simultaneously maximizing the number of {\it{bona fide}}cluster members while minimizing the number of contaminating interlopers.Moreover, rather than employing scaling relations, we calculate cluster massesindividually using the virial mass estimator. Since $\mathtt{GalWCat19}$ is alow-redshift cluster catalog we do not need to make any assumptions aboutevolution either in cosmological parameters or in the properties of theclusters themselves. Our constraints on \om ~and \sig ~are consistent and verycompetitive with those obtained from non-cluster abundance cosmological probessuch as Cosmic Microwave Background (CMB), Baryonic Acoustic Oscillation (BAO),and supernovae (SNe). The joint analysis of our cluster data withPlanck18+BAO+Pantheon gives \om ~$=0.315^{+0.013}_{-0.011}$ and \sig~$=0.810^{+0.011}_{-0.010}$.

Cosmological Constraint on $\Omega_m$ and $\sigma_8$ from Cluster Abundances using the $\mathtt{GalWCat19}$ Optical-Spectroscopic SDSS Catalog