Singular twisted links and singular twisted virtual braids

The concepts of the twisted knot theory and the virtual singular knot theory inspire the introduction of the singular twisted knot theory. This research presents comparable results for singular twisted links, such as the Alexander and Markov theorems derived from virtual knot theory. However, it differentiates itself from virtual singular knot theory by demonstrating that the number of Markov moves can be minimized within this framework. Furthermore, this paper introduces singular twisted virtual braids and explores their monoid structure. We also offer a monoid presentation and a reduced monoid presentation for singular twisted virtual braids.