Cosmological Constraint on $\Omega_m$ and $\sigma_8$ from Cluster
  Abundances using the $\mathtt{GalWCat19}$ Optical-Spectroscopic SDSS Catalog
  We derive cosmological constraints on the matter density, \om, and the
amplitude of fluctuations, \sig, using $\mathtt{GalWCat19}$, a catalog of 1800
galaxy clusters we identified in the Sloan Digital Sky Survey-DR13
spectroscopic data set using our GalWeight technique to determine cluster
membership \citep{Abdullah18,Abdullah19}. By analyzing a subsample of 756
clusters 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 normalization
relation of $\sigma_8= 0.43 \Omega_m^{-0.55}$. There are several unique aspects
to our approach: we use the largest spectroscopic data set currently available,
and we assign membership using the GalWeight technique which we have shown to
be 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 masses
individually using the virial mass estimator. Since $\mathtt{GalWCat19}$ is a
low-redshift cluster catalog we do not need to make any assumptions about
evolution either in cosmological parameters or in the properties of the
clusters themselves. Our constraints on \om ~and \sig ~are consistent and very
competitive with those obtained from non-cluster abundance cosmological probes
such as Cosmic Microwave Background (CMB), Baryonic Acoustic Oscillation (BAO),
and supernovae (SNe). The joint analysis of our cluster data with
Planck18+BAO+Pantheon gives \om ~$=0.315^{+0.013}_{-0.011}$ and \sig
~$=0.810^{+0.011}_{-0.010}$.
