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<p>Given a periodic splitting sequence of a measured train track, an Agol cycle is the part that constitutes a period up to the action of a pseudo-Anosov map and the rescaling by its dilatation. We consider a family of pseudo-Anosov maps on the 2-punctured torus and on the 5-punctured sphere and describe their Agol cycles explicitly. As an application, we classify conjugacy classes of pseudo-Anosov maps in the family.</p>

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Agol cycles of pseudo-Anosov maps on the 2-punctured torus and 5-punctured sphere

  • 期刊论文

  • 发表日期：

    2025年8月8日

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  • Jean-Baptiste Bellynck,
  • Eiko Kin

摘要

Given a periodic splitting sequence of a measured train track, an Agol cycle is the part that constitutes a period up to the action of a pseudo-Anosov map and the rescaling by its dilatation. We consider a family of pseudo-Anosov maps on the 2-punctured torus and on the 5-punctured sphere and describe their Agol cycles explicitly. As an application, we classify conjugacy classes of pseudo-Anosov maps in the family.