On Infinite Kuratowski Theorems

Abstract

Siri and Gvozdjak proved in [9] that the bananas surface, the pseudosurface consisting in the $2$-amalgamation of two spheres, does not admit a finite Kuratowski Theorem.

In this paper we prove that pseudosurfaces arising from the $n$-amalgamation of two closed surfaces, $n\ge 2$, do not admit a finite Kuratowski Theorem, by showing an infinite family of minimal non-embeddable graphs.