Local property of strong surfaces

A basic property of a simple closed surface is the Jordan property: the complement of the surface has two connected components. We call back-component any such component, and the union of a back-component and the surface a's called the closure of this back-component. In an earlier work, we introduced the notion of strong surface as a surface which satisfies a global homotopy property: the closure of a back-component is strongly homotopic to that back-component. It means that we can homotopically remove any subset of a strong surface from the closure of a back-component. It was proved that the simple closed 26-surfaces defined by Morgenthaler and Rosenfeld, and the simple closed 18-surfaces defined by one of the authors are both strong surfaces. In this paper, some necessary local conditions for strong 26-surfaces are presented. This is a first step towards a complete local characterization of these surfaces.