Tied links and invariants for singular links

Tied links and the tied braid monoid were introduced recently by authors used to define new invariants for classical links. Here, we give a version purely algebraic–combinatoric of With this prove that has decomposition like semi–direct group product. By using reprove Alexander Markov theorem links; also, introduce singular knots, certain families Homflypt type these are five–variables polynomials. Finally, study behavior invariants; in particular, show our distinguish non isotopic indistinguishable Paris–Rabenda invariant.