A degree-zero, monotone, surjective self-map of the Pontryagin surface

Abstract

. This paper presents an example, as promised by the title, of a degree-zero, monotone, surjective map of the standard Pontryagin surface to itself. This exposes the need for some hypothesis concerning degree in results about when monotone self-maps of the Pontryagin surface can be approximated by homeomorphisms.