Invariants of multi-linkoids

TL;DR

This paper extends the concept of knotoids to multi-linkoids on surfaces and investigates their invariants, including polynomial and skein invariants, to understand their mathematical properties.

Contribution

It introduces the notion of multi-linkoids and studies their invariants, expanding the framework of knotoid theory to more complex structures on surfaces.

Findings

Defined multi-linkoids as an extension of knotoids.

Analyzed invariants like Kauffman bracket and skein modules for multi-linkoids.

Connected invariants with generalized $ heta$-graphs.

Abstract

In this paper, we extend the definition of a knotoid that was introduced by Turaev, to multi-linkoids that consist of a number of knot and knotoid components. We study invariants of multi-linkoids that lie in a closed orientable surface, namely the Kauffman bracket polynomial, ordered bracket polynomial, the Kauffman skein module, and the $T$-invariant in relation with generalized $\Theta$-graphs.