Orientation-reversing involutions of the genus 3 Arnoux-Yoccoz surface and related surfaces

Abstract

We present a new description of the genus 3 Arnoux--Yoccoz translation surface in terms of its Delaunay polygons and show that, up to affine equivalence, it belongs to two families of surfaces whose isometry groups include the dihedral group of the square.

arXiv comment11 pages, incl. references; 7 figures; to appear in the Proceedings of the Fourth Alhfors-Bers Colloquium; incorporates suggestions by referee