The singular twisted virtual pure braid monoid and two related submonoids are characterized as kernels of epimorphisms to the symmetric group, with explicit presentations, plus a monoid-to-group embedding and representation extension result.
Singular twisted links and singular twisted virtual braids
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abstract
The concepts of twisted knot theory and singular knot theory inspire the introduction of singular twisted knot theory. This study showcases similar findings for singular twisted links, including the Alexander theorem and the Markov theorem derived from knot theory. Moreover, in this paper we define singular twisted virtual braids and their monoid structure. Additionally, we provide both a monoid and a reduced monoid presentation for singular twisted virtual braids.
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The monoid structure of singular twisted virtual braids
The singular twisted virtual pure braid monoid and two related submonoids are characterized as kernels of epimorphisms to the symmetric group, with explicit presentations, plus a monoid-to-group embedding and representation extension result.