Classification of Lagrangian Fibrations over a Klein Bottle

Abstract

This paper completes the classification of regular Lagrangian fibratiopns over compact surfaces. \cite{misha} classifies regular Lagrangian fibrations over ${\mathbb{T}}^2$. The main theorem in \cite{hirsch} is used in order to classify integral affine structures on the Klein bottle $K^2$ and, hence, regular Lagrangian fibrations over this space.

16 pages, to appear in Geometriae Dedicata