2015/05/25 by Maria Chlouveraki, Jesús Juyumaya, Chlouveraki, Maria +5 · 2 citations
Mathematics · #20C08 #20F36 #20F38 #57M25 #57M27 #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.1505.06666
openalex publication_date 2015/05/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we announce the existence of a family of new 2-variable\npolynomial invariants for oriented classical links defined via a Markov trace\non the Yokonuma-Hecke algebra of type A. Yokonuma-Hecke algebras are\ngeneralizations of Iwahori-Hecke algebras, and this family contains the\nHomflypt polynomial, the famous 2-variable invariant for classical links\narising from the Iwahori-Hecke algebra of type A. We show that these\ninvariants are topologically equivalent to the Homflypt polynomial on knots,\nbut not on links, by providing pairs of Homflypt-equivalent links that are\ndistinguished by our invariants. In order to do this, we prove that our\ninvariants can be defined diagrammatically via a special skein relation\ninvolving only crossings between different components. We further generalize\nthis family of invariants to a new 3-variable skein link invariant which is\nstronger than the Homflypt polynomial. Finally, we present a closed formula for\nthis invariant, by W.B.R. Lickorish, which uses Homflypt polynomials of\nsublinks and linking numbers of a given oriented link.\n