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The surface singular braid monoid corresponds to marked graph diagrams ofknotted surfaces in braid form. In a quest to resolve linearity problem forthis monoid, we will show that if it is defined on at least two or at leastthree strands, then its two or respectively three dimensional representationsare not faithful. We will also derive new presentations for the surfacesingular braid monoid, one with reduced the number of defining relations, andthe other with reduced the number of its singular generators. We includesurface singular braid formulations of all knotted surfaces in Yoshikawa'stable.

Presentations and representations of surface singular braid monoids