Index Polynomials for Virtual Tangles

TL;DR

This paper extends the index polynomial invariant to virtual tangles, introducing three new polynomial invariants and exploring their fundamental properties.

Contribution

It generalizes the index polynomial to virtual tangles and defines three new polynomial invariants with basic properties.

Findings

Three polynomial invariants for virtual tangles are introduced.

The basic properties of these invariants are analyzed.

The generalization broadens the applicability of index polynomials.

Abstract

We generalize the index polynomial invariant to the case of virtual tangles. Three polynomial invariants result from this generalization; we give a brief overview of their definition and some basic properties.