Moscow Mathematical Journal

Volume 25, Issue 4, October–December 2025 pp. 511–534.

Invariants for Singular Links via the Two Parameter bt-Algebra

Authors: Marcelo Flores (1) and Christopher Roque-Marquez (2)
Author institution:(1) Instituto de Matemáticas, Universidad de Valparaíso, Gran Bretaña 1111, Valparaíso 2340000, Chile
(2) Centro de Investigación y Docencia Económicas A.C., Carretera México-Toluca No. 3655, Ciudad de México 01210, México

Summary:

We construct a new invariant of singular links through representations of the singular braid monoid into the two parameters bt-algebra. Additionally, we recover this invariant by using the approach of Paris and Rabenda. Hence, we introduce the so called two parameter Singular bt-algebra. Finally, we provide the skein relations that define our invariant, and we prove that this invariant is more powerful than previous invariants of singular links in literature.

2020 Math. Subj. Class. Primary: 57K12, 57K14, 20F36.

Keywords: Singular links, singular braid monoid, bt-algebra, tied links.

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