Trace field degrees in the Torelli group - CNRS - Centre national de la recherche scientifique
Pré-Publication, Document De Travail Année : 2024

Trace field degrees in the Torelli group

Erwan Lanneau
Livio Liechti
  • Fonction : Auteur

Résumé

We show that for $g\ge 2$, all integers $1 \le d \le 3g-3$ arise as trace field degrees of pseudo-Anosov mapping classes in the Torelli group of the closed orientable surface of genus $g$. Our method uses the Thurston-Veech construction of pseudo-Anosov maps, and we provide examples where the stretch factor has algebraic degree any even number between two and $6g-6$. This validates a claim by Thurston from the 1980s.

Dates et versions

hal-04745503 , version 1 (20-10-2024)

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Erwan Lanneau, Livio Liechti. Trace field degrees in the Torelli group. 2024. ⟨hal-04745503⟩
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