On the link invariants from the Yokonuma-Hecke algebras

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In this paper we study properties of the Markov trace trd and the specialized trace trd,D on the Yokonuma-Hecke algebras, such as behaviour under inversion of a word, connected sums and mirror imaging. We then define invariants for framed, classical and singular links through the trace trd,D and also invariants for transverse links through the trace trd. In order to compare the invariants for classical links with the Homflypt polynomial we develop computer programs and we evaluate them on several Homflypt-equivalent pairs of knots and links. Our computations lead to the result that these invariants are topologically equivalent to the Homflypt polynomial on knots. However, they do not demonstrate the same behaviour on links.