Graph skein modules and symmetry of spatial graphs

TL;DR

This paper computes the graph skein algebra of a punctured disk with two holes and uses it to derive conditions for spatial graphs to have prime order symmetries, extending previous results.

Contribution

It introduces new skein algebra computations and applies them to establish symmetry obstructions for spatial graphs, broadening understanding of their symmetrical properties.

Findings

Computed the graph skein algebra of a punctured disk with two holes.

Established necessary conditions for spatial graphs to have prime order symmetries.

Extended earlier results on symmetric spatial graphs.

Abstract

In this paper, we compute the graph skein algebra of the punctured disk with two holes. Then, we apply the graph skein techniques developed here to establish necessary conditions for a spatial graph to have a symmetry of order $p$, where $p$ is a prime. The obstruction criteria introduced here extend some results obtained earlier for symmetric spatial graphs.