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Formal Markoff maps are positive

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Abstract

This note defines a family of Laurent polynomials indexed in \({\mathbb{P}^1\mathbb{Q}}\) which generalize the Markoff numbers and relate to the character variety of the one-cusped torus. We describe which monomials appear in each polynomial and prove all the coefficients are positive integers. We also conjecture a generalization of that positivity result.

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Authors and Affiliations

  1. Laboratoire de mathématiques, bâtiment 425, CNRS: UMR 8628, Université Paris—Sud, Orsay cedex, 91405, France

    François Guéritaud

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  1. François Guéritaud
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Correspondence to François Guéritaud.

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Guéritaud, F. Formal Markoff maps are positive. Geom Dedicata 134, 203–216 (2008). https://doi.org/10.1007/s10711-008-9256-y

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  • DOI: https://doi.org/10.1007/s10711-008-9256-y

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