**Title:** Rel leaves of the Arnoux-Yoccoz surfaces

**Speaker:** Pat Hooper

**Speaker Info:** CUNY

**Brief Description:**

**Special Note**:

**Abstract:**

A translation surface is a compact surface modeled on the Euclidean plane where transition functions are translations. The Gauss-Bonnet theorem forces the appearance of cone singularities whose angles are integer multiples of 2π whenever the genus of the surface exceeds 1. Informally, a rel deformation of a translation surface is obtained by moving singularities relative to each other. Such a deformation is horizontal, if the relative motion is horizontal.We will discuss a case when the closure of the set of surfaces obtained by horizontal rel deformations of a fixed surface is a ray exiting every compact collection of surfaces. In contrast, the closure of the set of surfaces obtained by all rel deformations of this surface is as large as possible (the full connected component of surfaces of the same type). This is joint work with Barak Weiss.

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