There are no periodic Wright maps

Abstract

This paper proves that every periodic automorphism of a closed hyperbolic surface S sends some curve to a nearly disjoint curve. In particular, periodic maps cannot have the property that every curve fills with its image, so no such map can give a positive answer to a question of Wright. This paper also answers a question of Schleimer about irreducible periodic surface maps.

7 pages, 1 figure. v2: updated references