Matrix Formulae and Skein Relations for Quasi-Cluster Algebras
Combinatorics
2026-03-02 v2 Geometric Topology
Rings and Algebras
Abstract
In this paper, we give matrix formulae for non-orientable surfaces that provide the Laurent expansion for quasi-cluster variables, generalizing the orientable surface matrix formulae by Musiker-Williams. We additionally use our matrix formulas to prove the skein relations for the elements in the quasi-cluster algebra associated to curves on the non-orientable surface.
Keywords
Cite
@article{arxiv.2312.06148,
title = {Matrix Formulae and Skein Relations for Quasi-Cluster Algebras},
author = {Cody Gilbert and McCleary Philbin and Kayla Wright},
journal= {arXiv preprint arXiv:2312.06148},
year = {2026}
}