arXiv Open Access 2020

A characterization of pseudo-Anosov mapping classes via tropical cluster transformations

Tsukasa Ishibashi Shunsuke Kano

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Abstrak

We give a characterization of generic pseudo-Anosov mapping classes purely in terms of their expressions in the shear coordinates, thus giving an answer to a problem raised by Papadopoulos--Penner [PP93]. This characterization has a cluster algebraic generalization called the sign stability introduced in [IK21]. By combining with the results in [IK21], we see that the algebraic entropies of the cluster $\mathcal{A}$- and $\mathcal{X}$-transformations induced by a generic pseudo-Anosov mapping class both coincide with its topological entropy.

Topik & Kata Kunci

math.GT math.CO math.DS

Penulis (2)

Tsukasa Ishibashi

Shunsuke Kano

Format Sitasi

APA MLA BibTeX

Ishibashi, T., Kano, S. (2020). A characterization of pseudo-Anosov mapping classes via tropical cluster transformations. https://arxiv.org/abs/2010.05214

Akses Cepat

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Informasi Jurnal

Tahun Terbit: 2020
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓