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2017•arXiv (Cornell University)Open access

On commensurability of quadratic differentials

Hidetoshi Masai

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Abstract

We consider commensurability of quadratic differentials on surfaces. Each commensurability class has a natural order by the covering relation. We show that each commensurability class contains a unique (orbifold) element. We also discuss the relationship between commensurability of quadratic differentials and fibered commensurability, a notion introduced by Calegari-Sun-Wang.

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We consider commensurability of quadratic differentials on surfaces. Each commensurability class has a natural order by the covering relation. We show that each commensurability class contains a unique (orbifold) element. We also discuss the relationship between commensurability of quadratic differentials and fibered commensurability, a notion introduced by Calegari-Sun-Wang.

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Available abstract

We consider commensurability of quadratic differentials on surfaces. Each commensurability class has a natural order by the covering relation. We show that each commensurability class contains a unique (orbifold) element. We also discuss the relationship between commensurability of quadratic differentials and fibered commensurability, a notion introduced by Calegari-Sun-Wang.

Key concepts: Commensurability (mathematics), Quadratic equation, Orbifold, Pure mathematics, Mathematics, Geometry

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