The hull of Rudin’s Klein bottle

Abstract

In 1981 Walter Rudin exhibited a totally real embedding of the Klein bottle into C 2 \mathbb {C}^2 . We show that the polynomially convex hull of Rudin’s Klein bottle contains an open subset of C 2 \mathbb {C}^2 . We also describe another totally real Klein bottle in C 2 \mathbb {C}^2 whose hull has topological dimension equal to three.