Formal Markoff maps are positive |
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Authors: | François Guéritaud |
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Affiliation: | (1) Laboratoire de mathématiques, batiment 425, CNRS: UMR 8628, Université Paris—Sud, Orsay cedex, 91405, France |
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Abstract: | This note defines a family of Laurent polynomials indexed in 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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Keywords: | Markoff equation Once-punctured torus Laurent polynomials |
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