A meridian lemma for fully alternating links in thickened surfaces

TL;DR

This paper extends Menasco's meridian lemma to fully alternating links in thickened orientable surfaces of positive genus, providing new insights into their geometric structure.

Contribution

It introduces a meridian lemma for fully alternating links in thickened surfaces, generalizing previous results from $S^3$ to higher genus surfaces.

Findings

Established a meridian lemma for fully alternating links in thickened surfaces.

Generalized Menasco's result from $S^3$ to higher genus surfaces.

Enhanced understanding of the topology of fully alternating links.

Abstract

Menasco showed that a closed surface in the complement of a non-split prime alternating link in $S^3$ contains a circle isotopic in the link complement to a meridian of the links. This result is known as the meridian lemma for alternating links. We give a meridian lemma for the class of fully alternating links in the thickened orientable surfaces of positive genus.