Topological Classification of Lagrangian Fibrations

TL;DR

This paper introduces topological invariants for regular Lagrangian fibrations based on integral affine structures and classifies symplectic types of such fibrations over the real projective line with fixed monodromy, extending previous constructions.

Contribution

It defines new topological invariants for Lagrangian fibrations and provides a classification of their symplectic types over  with fixed monodromy, generalizing Bates' work.

Findings

Topological invariants coincide with known classes.

Classification of symplectic types over  with fixed monodromy.

Extension of Bates' construction to broader cases.

Abstract

We define topological invariants of regular Lagrangian fibrations using the integral affine structure on the base space and we show that these coincide with the classes known in the literature. We also classify all symplectic types of Lagrangian fibrations with base $\rpr$ and fixed monodromy representation, generalising a construction due to Bates.