Tied links and invariants for singular links

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2021

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Elsevier

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item.page.issne

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Instituto de Matematicass

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Resumen

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

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TIED LINKS, SET PARTITION, BT–ALGEBRA, INVARIANTS FOR SINGULAR LINKS AND TIED, SINGULAR LINKS

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© 2021 Elsevier Inc. All rights reserved.

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