Invariants for singular links via the two parameter bt-algebra

TL;DR

This paper introduces a new, more powerful invariant for singular links using the two-parameter bt-algebra, constructed via singular braid monoid representations and skein relations.

Contribution

It develops the two-parameter Singular bt-algebra and demonstrates its effectiveness in defining a stronger invariant for singular links compared to existing methods.

Findings

The invariant is more powerful than previous singular link invariants.

The paper provides explicit skein relations for the invariant.

Recovery of the invariant via Paris and Rabenda's approach.

Abstract

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.