A series of coverings of the regular n-gon

Abstract

We define an infinite series of translation coverings of Veech's double-n-gon for odd n greater or equal to 5 which share the same Veech group. Additionally we give an infinite series of translation coverings with constant Veech group of a regular n-gon for even n greater or equal to 8. These families give rise to explicit examples of infinite translation surfaces with lattice Veech group.

A missing case in step 1 in the proof of Thm. 1 b was added. (To appear in Geometriae Dedicata.)

References in corpus (3)

• Dynamics on an infinite surface with the lattice property
• Generalized staircases: recurrence and symmetry
• Veech groups, irrational billiards and stable abelian differentials

Cited by in corpus (1)

• Loop subgroups of F_r and the image of their stabilizer subgroups in GL_r(Z)