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Super Markov numbers and signed double dimer covers
Published Web Location
https://doi.org/10.5070/C6.69939Abstract
We provide a superalgebraic analogue of Markov numbers, which are defined as the Grassmann integer solutions to the equation \(x^2 + y^2 + z^2 + (xy + yz + xz)\epsilon = 3(1+\epsilon)xyz\), as well as applications to the decorated super Teichmüller spaces associated to the once-punctured torus and certain annuli. We conclude with further directions for study.
Mathematics Subject Classifications: 13F60, 17A70, 30F60, 11D25, 05C70
Keywords: Markov numbers, Super Teichmüller space, snake graphs, double dimer covers