# Novikov's theorem in higher dimensions?

## TL;DR

This paper investigates whether higher-dimensional analogues of Novikov's theorem hold for strong symplectic foliations, providing a counterexample on a five-dimensional manifold that challenges the expected rigidity properties.

## Contribution

The paper constructs a five-dimensional example of a strong symplectic foliation that does not satisfy the analogue of Novikov's theorem, highlighting limitations of such rigidity results in higher dimensions.

## Key findings

- Counterexample on a 5D manifold with a strong symplectic foliation
- Shows failure of Novikov's theorem analogue in higher dimensions
- Introduces a foliated Lefschetz fibration as the example

## Abstract

Novikov's theorem is a rigidity result on the class of taut foliations on three-manifolds. For higher dimensional manifolds, foliations with a strong symplectic form have been suggested as the class of foliations having similar rigidity properties to taut foliations on three-manifolds. This leads to the natural question of whether strong symplectic foliations satisfy an analogue of Novikov's theorem. In this paper, we construct a five-dimensional manifold with a smooth foliation and a strong symplectic form that does not satisfy the expected analogue of Novikov's theorem. Our example is a foliated Lefschetz fibration.