Non-orientable 3-manifolds of surface-complexity one

Abstract

We classify all closed non-orientable ${\mathbb{P}}^2$-irreducible 3-manifolds obtained by identifying the faces of a cube. These turn out to be the closed non-orientable ${\mathbb{P}}^2$-irreducible 3-manifolds with surface-complexity one. We show that they are the four flat ones.

8 pages, 4 figures, 3 tables