Tied links and invariants for singular links

Francesca Aicardi; Jesus Juyumaya

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arXiv · 1807.10071

Tied links and invariants for singular links

Francesca Aicardi·Jesus Juyumaya

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Abstract

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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BibTeX RIS

Francesca Aicardi, Jesus Juyumaya. 2018-07-26. Tied links and invariants for singular links. https://arxiv.org/abs/1807.10071

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